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Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium "quench" process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications. [ABSTRACT FROM AUTHOR]

Utilization of metal tungsten (W) as the structural material or pressure scale requires accurate knowledge of the equation of state (EOS), which is far beyond the available experimental measurements. In the present work, a direct integral approach (DIA) with ultrahigh efficiency was applied to calculate the EOS of W up to 500 GPa and 3000 K with ab initio calculations. Compared with previous static compression experiments up to 150 GPa under room temperature and 35 GPa at high temperatures up to 1673 K, all the deviations of the calculated pressure are within or comparable to the uncertainty of experiments. Predictions for higher-temperature and simultaneously higher-pressure EOS up to 300 GPa and 3000 K differ slightly from the comprehensive analysis by Litasov et al. [J. Appl. Phys. 113, 133505 (2013)] via fitting available experimental data with the empirical equation. These results indicate that the EOS of crystal W obtained from DIA should be convincible, and DIA without any empirical or artificial parameters may find its wide applications for predicting thermodynamic properties of condensed matter in the future. [ABSTRACT FROM AUTHOR]

We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously projected onto their J = 0 rotational state by an "Eckart spring" that connects two adjacent beads in a ring polymer. Using this procedure, the tunneling splitting can be obtained from thermodynamic integration at just one (sufficiently low) temperature. Converged results are formally identical to the values that would have been obtained by solving the full rovibrational Schrödinger equation on a given Born–Oppenheimer potential energy surface. The new approach is showcased with simulations of hydronium and methanol, which are in good agreement with wavefunction-based calculations and experimental measurements. The method will be of particular use for the study of low-barrier methyl rotations and other floppy modes, where instanton theory is not valid. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the simple current orbifold of a rational Narain CFT (Narain RCFT). This is a method of constructing other rational CFTs from a given rational CFT, by 'orbifolding' the global symmetry formed by a particular primary fields (called the simple current). Our main result is that a Narain RCFT satisfying certain conditions can be described in the form of a simple current orbifold of another Narain RCFT, and we have shown how the discrete torsion in taking that orbifold is obtained. Additionally, the partition function can be considered a simple current orbifold with discrete torsion, which is determined by the lattice and the B-field. We establish that the partition function can be expressed as a polynomial, with the variables substituted by certain q -series. In a specific scenario, this polynomial corresponds to the weight enumerator polynomial of an error-correcting code. Using this correspondence to the code theory, we can relate the B-field, the discrete torsion, and the B-form to each other. [ABSTRACT FROM AUTHOR]

We prove that the number q (n) of partitions of n with distinct parts is log-concave for n ≥ 33 and satisfies the third-order Turán inequalities for n ≥ 121 conjectured by Craig and Pun. In doing so, we establish explicit error terms for q (n) and for q (n − 1) q (n + 1) / q (n) 2 based on Chern's asymptotic formulas for η -quotients. [ABSTRACT FROM AUTHOR]

Multifractality is a concept that extends locally the usual ideas of fractality in a system. Nevertheless, the multifractal approaches used lack a multifractal dimension tied to an entropy index like the Shannon index. This paper introduces a generalized Shannon index (GSI) and demonstrates its application in understanding system fluctuations. To this end, traditional multifractality approaches are explained. Then, using the temporal Theil scaling and the diffusive trajectory algorithm, the GSI and its partition function are defined. Next, the multifractal exponent of the GSI is derived from the partition function, establishing a connection between the temporal Theil scaling exponent and the generalized Hurst exponent. Finally, this relationship is verified in a fractional Brownian motion and applied to financial time series. In fact, this leads us to proposing an approximation called local fractional Brownian motion approximation, where multifractal systems are viewed as a local superposition of distinct fractional Brownian motions with varying monofractal exponents. Also, we furnish an algorithm for identifying the optimal q-th moment of the probability distribution associated with an empirical time series to enhance the accuracy of generalized Hurst exponent estimation. [ABSTRACT FROM AUTHOR]

For a positive integer t ≥ 2 , let b t (n) denote the number of t-regular partitions of a nonnegative integer n. Motivated by some recent conjectures of Keith and Zanello, we establish infinite families of congruences modulo 2 for b 9 (n) and b 19 (n) . We prove some specific cases of two conjectures of Keith and Zanello on self-similarities of b 9 (n) and b 19 (n) modulo 2. For t ∈ { 6 , 10 , 14 , 15 , 18 , 20 , 22 , 26 , 27 , 28 } , Keith and Zanello conjectured that there are no integers A > 0 and B ≥ 0 for which b t (A n + B) ≡ 0 (mod 2) for all n ≥ 0 . We prove that, for any t ≥ 2 and prime ℓ , there are infinitely many arithmetic progressions A n + B for which ∑ n = 0 ∞ b t (A n + B) q n ≢ 0 (mod ℓ) . Next, we obtain quantitative estimates for the distributions of b 6 (n) , b 10 (n) and b 14 (n) modulo 2. We further study the odd densities of certain infinite families of eta-quotients related to the 7-regular and 13-regular partition functions. [ABSTRACT FROM AUTHOR]

We study the n$n$‐point differentials corresponding to Kadomtsev–Petviashvili (KP) tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their ℏ2$\hbar ^2$‐deformations and expansions. Under the naturally required analytic assumptions, we prove certain higher loop equations that, in particular, contain the standard linear and quadratic loop equations, and thus imply the blobbed topological recursion. We also distinguish two large families of the Orlov–Scherbin partition functions that do satisfy the natural analytic assumptions, and for these families, we prove in addition the so‐called projection property and thus the full statement of the Chekhov–Eynard–Orantin topological recursion. A particular feature of our argument is that it clarifies completely the role of ℏ2$\hbar ^2$‐deformations of the Orlov–Scherbin parameters for the partition functions, whose necessity was known from a variety of earlier obtained results in this direction but never properly understood in the context of topological recursion. As special cases of the results of this paper, one recovers new and uniform proofs of the topological recursion to all previously studied cases of enumerative problems related to weighted double Hurwitz numbers. By virtue of topological recursion and the Grothendieck–Riemann–Roch formula, this, in turn, gives new and uniform proofs of almost all Ekedahl–Lando–Shapiro–Vainshtein (ELSV)‐type formulas discussed in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we provide an algorithm to detect linear congruences of p l k (n) , the number of MacMahon's k -rowed plane partitions, and give a quantitative result on the nonexistence of Ramanujan-type congruences of the k -rowed plane partition functions. We also show p (n , m) that the number of partitions at most m parts always admits linear congruences. [ABSTRACT FROM AUTHOR]

We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q ∈ [ 1 , 4) . Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of q than the FK-Ising model ( q = 2 ). Given the convergence of interfaces, the conjectural formulas for other values of q could be verified similarly with relatively minor technical work. The limit interfaces are variants of SLE κ curves (with κ = 16 / 3 for q = 2 ). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all q ∈ [ 1 , 4) , thus providing further evidence of the expected CFT description of these models. [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Impact of nonconvergence and various approximations of the partition function on the molecular column densities in the interstellar medium." The full text of the article is not available in HTML format. The authors acknowledge the contributions of Dr. Edgar Mendoza and the funding received from the European Union's Horizon 2020 research and innovation program. The authors of the article are M. Carvajal, C. Favre, I. Kleiner, C. Ceccarelli, E. A. Bergin, and D. Fedele. [Extracted from the article]

In this work we study families of ℤ2 orbifolds of toroidal conformal field theories based on both factorizable and non-factorizable target space tori. For these classes of theories, we analyze their moduli spaces, and compute their partition functions. Building on previous work, we express the calculated partition functions in terms of suitable Siegel-Narain theta functions that allow us to determine their ensemble averages. We express the derived averaged partition functions of the studied families of conformal field theories in a manifest modular invariant finite sum of products of real analytic Eisenstein series. We speculate on a tentative holographic three-dimensional dual bulk interpretations for the considered ℤ2 orbifold classes of ensembles of conformal field theories. [ABSTRACT FROM AUTHOR]

We define two types of Witten's zeta functions according to Cartan's classification of compact symmetric spaces. The type II is the original Witten zeta function constructed by means of irreducible representations of the simple compact Lie group U. The type I Witten zeta functions, we introduce here, are related to the irreducible spherical representations of U. They arise in the harmonic analysis on compact symmetric spaces of the form U/K, where K is the maximal subgroup of U. To construct the type I zeta function we calculate the partition functions of 2d YM theory with broken gauge symmetry using the Migdal–Witten approach. We prove that for the rank one symmetric spaces the generating series for the values of the type I functions with integer arguments can be defined in terms of the generating series of the Riemann zeta-function. [ABSTRACT FROM AUTHOR]

A (1 + 1)D unitary bosonic rational conformal field theory (RCFT) may be organized according to its genus, a tuple (c , C) consisting of its central charge c and a unitary modular tensor category C which describes the (2 + 1)D topological quantum field theory for which its maximally extended chiral algebra forms a holomorphic boundary condition. We establish a number of results pertaining to RCFTs in "small" genera, by which we informally mean genera with the central charge c and the number of primary operators r a n k (C) both not too large. We start by completely solving the modular bootstrap problem for theories with at most four primary operators. In particular, we characterize, and provide an algorithm which efficiently computes, the function spaces to which the partition function of any bosonic RCFT with r a n k (C) ≤ 4 must belong. Using this result, and leveraging relationships between RCFTs and holomorphic vertex operator algebras which come from "gluing" and cosets, we rigorously enumerate all bosonic theories in 95 of the 105 genera (c , C) with c ≤ 24 and r a n k (C) ≤ 4. This includes as (new) special cases the classification of chiral algebras with three primaries and c < 120/7 ∼ 17.14, and the classification of chiral algebras with four primaries and c < 62/3 ∼ 20.67. We then study two applications of our classification. First, by making use of chiral versions of bosonization and fermionization, we obtain the complete list of purely left-moving fermionic RCFTs with c < 23 as a corollary of the results of the previous paragraph. Second, using a (conjectural) concept which we call "symmetry/subalgebra duality," we precisely relate our bosonic classification to the problem of determining certain generalized global symmetries of holomorphic vertex operator algebras. [ABSTRACT FROM AUTHOR]

We discuss matters related to the point that topological quantization in the strong interaction is a consequence of an infinite spacetime volume. Because of the ensuing order of limits, i.e., infinite volume prior to summing over topological sectors, C P is conserved. Here, we show that this reasoning is consistent with the construction of the path integral from steepest-descent contours. We reply to some objections that aim to support the case for C P violation in strong interactions that are based on the role of the C P -odd theta-parameter in three-form effective theories, the correct sampling of all configurations in the dilute instanton gas approximation and the volume dependence of the partition function. We also show that the chiral effective field theory derived from taking the volume to infinity first is in no contradiction with analyses based on partially conserved axial currents. [ABSTRACT FROM AUTHOR]

We consider the estimation of the marginal likelihood in Bayesian statistics, with primary emphasis on Gaussian graphical models, where the intractability of the marginal likelihood in high dimensions is a frequently researched problem. We propose a general algorithm that can be widely applied to a variety of problem settings and excels particularly when dealing with near log-concave posteriors. Our method builds upon a previously posited algorithm that uses MCMC samples to partition the parameter space and forms piecewise constant approximations over these partition sets as a means of estimating the normalizing constant. In this paper, we refine the aforementioned local approximations by taking advantage of the shape of the target distribution and leveraging an expectation propagation algorithm to approximate Gaussian integrals over rectangular polytopes. Our numerical experiments show the versatility and accuracy of the proposed estimator, even as the parameter space increases in dimension and becomes more complicated. [ABSTRACT FROM AUTHOR]

K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences in black hole physics and in number theory. To a K3 surface, string theory associates an Elliptic genus, a certain partition function directly related to the theory of Jacobi modular forms. A multiplicative lift of the Elliptic genus produces another modular object, an Igusa cusp form, which is the generating function of BPS invariants of K3 × E . In this note, we will discuss a refinement of this chain of ideas. The Elliptic genus can be generalized to the so-called Hodge-Elliptic genus which is then related to the counting of refined BPS states of K3 × E . We show how such BPS invariants can be computed explicitly in terms of different versions of the Hodge-Elliptic genus, sometimes in closed form, and discuss some generalizations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two types of U(1)-gauge field theories on G 2 -manifolds. One is the U(1)-Yang–Mills theory which admits the classical instanton solutions. We show that G 2 -manifolds emerge from the anti-self-dual U(1) instantons, which is an analogy of Yang's result for Calabi–Yau manifolds. The other one is the higher-order U(1)-Chern–Simons theory as a generalization of Kähler–Chern–Simons theory. We introduce the notion of higher-order U(1)-instanton, as the vacuum configurations of higher-order U(1)-Chern–Simons theory. By suitable choice of gauge and regularization technique, we calculate the partition function under semiclassical approximation. Finally, to make sure of the invariance at quantum level under the large gauge transformations, we use Deligne–Beilinson cohomology theory to give the higher-order U(1)-Chern–Simons actions (U(1)-BF-type actions) for nontrivial U(1)-principle bundles. [ABSTRACT FROM AUTHOR]

Systems with a multistable energy landscape are widespread in physics, biophysics, technology, and materials science. They are strongly influenced by thermal fluctuations and external mechanical actions that can be applied at different rates, moving the system from equilibrium to non-equilibrium regimes. In this paper, we focus on a simple system involving a single breaking phenomenon to describe the various theoretical approaches used to study these problems. To begin with, we propose the exact solution at thermodynamic equilibrium based on the calculation of the partition function without approximations. We then introduce the technique of spin variables, which is able to simplify the treatment even for systems with a large number of coordinates. We then analyze the energy balance of the system to better understand its underlying physics. Finally, we introduce a technique based on transition state theory useful for studying the non-equilibrium dynamical regimes of these systems. This method is appropriate for the evaluation of rate effects and hysteresis loops. These approaches are developed for both the Helmholtz ensemble (prescribed extension) and the Gibbs ensemble (applied force) of statistical mechanics. The symmetry and duality of these two ensembles is discussed in depth. While these techniques are used here for a simple system with theoretical purposes, they can be applied to complex systems of interest for several physical, biophysical, and technological applications. [ABSTRACT FROM AUTHOR]

The (k , i) -singular overpartitions, combinatorial objects introduced by Andrews in 2015, are known to satisfy Ramanujan-type congruences modulo any power of prime coprime to 6 k. In this paper we consider the parity of the number C ‾ k , i (n) of (k , i) -singular overpartitions of n. In particular, we give a sufficient condition on even values of k so that the values of C ‾ 4 k , k (n) are almost always even. Furthermore, we show that for odd values of k ≤ 23 , k ≠ 19 , certain subsequences of C ‾ 4 k , k (n) are almost always even. [ABSTRACT FROM AUTHOR]

In this work, the pressure- and temperature-dependent reaction rate constants for the hydrogen abstraction and addition of hydroxyl radicals to the unsaturated cyclopentene were studied. Geometries and vibrational frequencies of reactants, products, and transition states were calculated using density functional theory, with single-point energy corrections determined at the domain-based local pair natural orbital-coupled-cluster single double triple/cc-pVTZ-F12 level. The high-pressure limit rate constants were calculated using the canonical variational transition state theory with the small-curvature tunneling approximation. The vibrational partition functions were corrected by the effects of torsional and ring-puckering anharmonicities of the transition states and cyclopentene, respectively. Variational effects are shown to be relevant for all the hydrogen abstraction reactions. The increasing of the rate constants by tunneling is significant at temperatures below 500 K. The pressure dependence on the rate constants of the addition of OH • to cyclopentene was calculated using the system-specific quantum Rice–Ramsperger–Kassel model. The high-pressure limit rate constants decrease with increasing temperature in the range 250–1000 K. The falloff behavior was studied at several temperatures with pressures varying between 10−3 and 103 bar. At temperatures below 500 K, the effect of the pressure on the addition rate constant is very modest. However, at temperatures around and above 1000 K, taking pressure into account is mandatory for an accurate rate constant calculation. Branching ratio analyses reveal that the addition reaction dominates at temperatures below 500 K, decreasing rapidly at higher temperatures. Arrhenius parameters are provided for all reactions and pressure dependent Arrhenius parameters are given for the addition of OH • to cyclopentene. [ABSTRACT FROM AUTHOR]

The classification of three-center two-electron (3c2e) bonds into supported (closed) or unsupported (open) was proposed by Lipscomb in his work on boranes and extended to transition metal complexes by Bau and co-workers. The species in which the interactions of the terminal atoms are negligible are called "unsupported bonds." Examples of chemical species that are said to exhibit such bonds are Li2H+, Na2H+, B2H7−, Al2(CH3)7−, and [(μ2-H)Cr2(CO)10]− although the general criterion for distinguishing these types of bonds is somewhat qualitative. Besides providing a unifying view of the nature of the chemical bond, in terms of quantum interference among electronic states, the Generalized Product Function Energy Partitioning method through the Interference Energy Analysis (IEA) is also potentially capable of providing a rigorous ground to the concept of supported bonds by looking at the specific interference energies between the orbital pairs associated with the bond. The IEA was performed in the species Li2H+, Na2H+, B2H7−, C2H7−, Al2H7−, and [(μ2-H)Cr2(CO)10]−, as well as along the reaction path Li2H+ → Li2+ + H. The results shown that in all studied A–B–C bonds, the A–C interactions are as important as the A–B/B–C ones, leading to the conclusion that all studied 3c2e bonds are "supported," in the sense that the A–C interaction is not negligible. The particularity of those species in preferring linear geometry is completely explained by quasi-classical effects, more specifically, by minimization of the electron–electron and nucleus–nucleus repulsions. [ABSTRACT FROM AUTHOR]

This paper deals with both the higher order Turán inequalities and the Laguerre inequalities for quasi-polynomial-like functions that are expressions of the form f (n) = c l (n) n l + ⋯ + c d (n) n d + o (n d) , where d , l ∈ N and d ⩽ l . A natural example of such a function is the A-partition function p A (n) , which enumerates the number of partitions of n with parts in the fixed finite multiset A = { a 1 , a 2 , ... , a k } of positive integers. For an arbitrary positive integer d, we present efficient criteria for both the order d Turán inequality and the dth Laguarre inequality for quasi-polynomial-like functions. In particular, we apply these results to deduce non-trivial analogues for p A (n) . [ABSTRACT FROM AUTHOR]

We introduce the edge Schur functions E λ that are defined as a generating series over edge labeled tableaux. We formulate E λ as the partition function for a solvable lattice model, which we use to show they are symmetric polynomials and derive a Cauchy-type identity with factorial Schur polynomials. Finally, we give a crystal structure on edge labeled tableau to give a positive Schur polynomial expansion of E λ and show it intertwines with an uncrowding algorithm. [ABSTRACT FROM AUTHOR]

Underground flow in fractured aquifers depends on the connectivity of the fractures, considered as a set of conduits and the main drainage axes. Quantitative analysis of fracture networks using multifractal characterisation therefore provides the backbone for assessing the connectivity of these networks. The aim of our work is to carry out a multifractal characterisation of lineament networks while performing related geometric, spectral and fractal analyses. The approach used is based on the box counting method to estimate the multifractal spectrum using the method of moments. The generalized fractal dimensions were estimated using the partition function and the multifractal spectrum using the Legendre transform. The work was carried out using a calculation code that we developed ourselves and that we named: 2D Calculation Code for Multifractal Analysis of Fracture Networks (2D-MAFN).Four lineament maps at different scales were analyzed, corresponding to the Upper Jurassic and Cretaceous geological formations of the El Gada region in the Central Algerian Saharan Atlas. The geometric analysis of the lineament networks showed good consistency between the lineament networks and the geological structure of the Atlas Range and its fault network. It also showed that the distribution of the lengths of the lineaments fits the power law. This analysis also revealed that, on a larger scale, diffuse fracturing appears to be more prevalent. In addition, the spectral analysis, through the decrease in spectral power according to a power law, characterizes a self-similar behavior and already seems to prove the scale invariance of the lineaments. The fractal dimension values obtained reflect the extent of fracturing and the degree of complexity of the network of lineaments. These values show that the lineaments are also well correlated with each other. The partition functions show that the points line up on the adjustment lines according to a law characteristic of multifractal behavior. In addition, the curves of generalized dimensions as a function of moments show a clear decrease, highlighting the multifractal nature of the fracturing process. In addition, the multifractal spectra in the form of bell curves also confirm the multifractal process for the four lineament networks analyzed. The results obtained are very encouraging and open up the prospects of modelling fracture networks for a variety of purposes, including assessing the connectivity of a fracture network. [ABSTRACT FROM AUTHOR]

We explore the thermal characteristics of fermionic fields with a nonminimal coupling in one, two, and three dimensions using the framework of superstatistics theory. We consider three distinct distributions: the gamma distribution, the lognormal distribution, and the F distribution. Each of these distributions is governed by a specific probability density function. To calculate the partition function, we use the Euler–Maclaurin formula, specifically in the low-energy asymptotic approximation of superstatistics. This calculation takes the remainder term into consideration. In each scenario, using the derived partition functions, we analyze the variations in entropy and specific heat with varying temperatures and the universal parameter denoted as . In general, we observe that increasing the value of enhances all the curves. Additionally, we note that entropy values tend to increase as the temperature decreases, and tend to decrease as the parameter increases. [ABSTRACT FROM AUTHOR]

The gravitational path integral can be used to compute the number of black hole states for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of (−1)F. In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of (−1)F. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities. [ABSTRACT FROM AUTHOR]

We consider the refined Schur superconformal index of 4d N = 4 U(N) SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using indirect superconformal algebra considerations and analytic continuation of fugacities. This correction is the leading non-perturbative correction to the index at large N and we reproduce it from the semiclassical partition function of quantum D3 brane wrapped on S1 × S3 in a twisted modification of the AdS5 × S5 string background, depending on the index R-symmetry fugacity. Our calculation does not exploit directly supersymmetry. It is based on the determination of the partition function of the various bosonic and fermionic fluctuations on the wrapped brane whose action is conformal with specific constant holonomies along thermal cycle. We show how those partition functions may be obtained by adapting the operator counting method of Cardy to the twisted background. [ABSTRACT FROM AUTHOR]

At first glance, thermodynamic properties of gravity with asymptotically AdS conditions and those with box boundary conditions, where the spatial section of the boundary is a sphere of finite radius, appear similar. Both exhibit a similar phase structure and Hawking-Page phase transition. However, when we introduce a U(1) gauge field to the system, discrepancies in thermodynamic properties between the two cases has been reported in [7] (JHEP 11 (2016) 041). In this paper, by accepting the assumption that all Euclidean saddles contribute to the partition function, I found that these discrepancies are resolved due to the contribution from the "bag of gold (BG)," which is the class of Euclidean geometries whose area of bolt is bigger than that of the boundary. As a result, the Hawking-Page phase structure is restored, with the unexpected properties that the upper bound of thermodynamic entropy is always larger than the boundary area divided by 4G when the chemical potential is non-zero, and that such high entropy states are realized at sufficiently high temperature. [ABSTRACT FROM AUTHOR]

We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of d, N × N matrices invariant under the adjoint action of the symmetric group SN. The approach is general to any discrete group. For a system of harmonic oscillators, i.e. for the non-interacting case, the partition function is given by the Molien-Weyl formula times the zero-point energy contribution. We further generalise the result to a system of non-square and complex matrices transforming under arbitrary representations of the gauge group. [ABSTRACT FROM AUTHOR]

The Euclidean path integral is compared to the thermal (canonical) partition function in curved static space-times. It is shown that if spatial sections are non-compact and there is no Killing horizon, the logarithms of these two quantities differ only by a term proportional to the inverse temperature, that arises from the vacuum energy. When spatial sections are bordered by Killing horizons the Euclidean path integral is not equal to the thermal partition function. It is shown that the expression for the Euclidean path integral depends on which integral is taken first: over coordinates or over momenta. In the first case the Euclidean path integral depends on the scattering phase shift of the mode and it is UV diverge. In the second case it is the total derivative and diverge on the horizon. Furthermore we demonstrate that there are three different definitions of the energy, and the derivative with respect to the inverse temperature of the Euclidean path integral does not give the value of any of these three types of energy. We also propose the new method of computation of the Euclidean path integral that gives the correct equality between the Euclidean path integral and thermal partition function for non-compact spaces with and without Killing horizon. [ABSTRACT FROM AUTHOR]

We study the twisted elliptic genera of 2d (0, 4) SCFTs associated with the BPS strings in the twisted circle compactification of 6d rank-one (1, 0) SCFTs. Such objects can arise when the 6d gauge algebra allows outer automorphism, thus are classified by twisted affine Lie algebras. We study several fascinating aspects of the twisted elliptic genera including 2d localization, twisted elliptic blowup equations, Higgsing and spectral flow symmetry. We derive a recursion formula with respect to the number of strings to exactly compute the twisted elliptic genera. We also investigate the modular bootstrap of twisted one-string elliptic genera and find the modularity of congruence subgroups Γ1(N) naturally appears with possible N = 2, 3, 4. Geometrically, our study solves the refined BPS partition functions of the underlying genus-one fibered Calabi-Yau threefolds with N-section. [ABSTRACT FROM AUTHOR]

We provide a first principles derivation of the supersymmetric Casimir energy of N = 1 SCFTs in four dimensions using the supercharge algebra on general conformal supergravity backgrounds that admit Killing spinors. The superconformal Ward identities imply that there exists a continuous family of conserved R-currents on supersymmetric backgrounds, as well as a continuous family of conserved currents for each conformal Killing vector. These continuous families interpolate between the consistent and covariant R-current and energy-momentum tensor. The resulting Casimir energy, therefore, depends on two continuous parameters corresponding to the choice of conserved currents used to define the energy and R-charge. This ambiguity is in addition to any possible scheme dependence due to local terms in the effective action. As an application, we evaluate the general expression for the supersymmetric Casimir energy we obtain on a family of backgrounds with the cylinder topology ℝ × S3 and admitting a single Majorana supercharge. Our result is a direct consequence of the supersymmetry algebra, yet it resembles more known expressions for the non-supersymmetric Casimir energy on such backgrounds and differs from the supersymmetric Casimir energy obtained from the zero temperature limit of supersymmetric partition functions. We defer a thorough analysis of the relation between these results to future work. [ABSTRACT FROM AUTHOR]

We study the logarithmic corrections to various CFT partition functions in the context of the AdS4/CFT3 correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordström black holes in AdS4. Our results also have important implications for effective field theory coupled to gravity in AdS4 and for the existence of scale-separated AdS4 vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields. [ABSTRACT FROM AUTHOR]

We compute the equivariant partition function of the six-dimensional M-string SCFTs on a background with the topology of a product of a two-dimensional torus and an ALE singularity. We determine the result by exploiting BPS strings probing the singularity, whose worldvolume theories we determine via a chain of string dualities. A distinguished feature we observe is that for this class of background the BPS strings' worldsheet theories become relative field theories that are sensitive to finer discrete data generalizing to 6d the familiar choices of flat connections at infinity for instantons on ALE spaces. We test our proposal against a conjectural 6d N = (1, 0) generalization of the Nekrasov master formula, as well as against known results on ALE partition functions in four dimensions. [ABSTRACT FROM AUTHOR]

Given the marked variation in abiotic and biotic conditions between day and night, many species specialise their physical activity to being diurnal or nocturnal, and it was long thought that these strategies were commonly fairly fixed and invariant. The term 'cathemeral', was coined in 1987, when Tattersall noted activity in a Madagascan primate during the hours of both daylight and darkness. Initially thought to be rare, cathemerality is now known to be a quite widespread form of time partitioning amongst arthropods, fish, birds, and mammals. Herein we provide a synthesis of present understanding of cathemeral behaviour, arguing that it should routinely be included alongside diurnal and nocturnal strategies in schemes that distinguish and categorise species across taxa according to temporal niche. This synthesis is particularly timely because (i) the study of animal activity patterns is being revolutionised by new and improved technologies; (ii) it is becoming apparent that cathemerality covers a diverse range of obligate to facultative forms, each with their own common sets of functional traits, geographic ranges and evolutionary history; (iii) daytime and nighttime activity likely plays an important but currently neglected role in temporal niche partitioning and ecosystem functioning; and (iv) cathemerality may have an important role in the ability of species to adapt to human‐mediated pressures. [ABSTRACT FROM AUTHOR]

We identify Whittaker vectors for W k (g) -modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of G-bundles over P 2 for G a complex simple Lie group, can be computed by a non-commutative version of the Chekhov–Eynard–Orantin topological recursion. We formulate the connection to higher Airy structures for Gaiotto vectors of type A, B, C, and D, and explicitly construct the topological recursion for type A (at arbitrary level) and type B (at self-dual level). On the physics side, it means that the Nekrasov partition function for pure N = 2 four-dimensional supersymmetric gauge theories can be accessed by topological recursion methods. [ABSTRACT FROM AUTHOR]

We introduce the topologically twisted index for four-dimensional N = 1 gauge theories quantized on AdS 2 × S 1 . We compute the index by applying supersymmetric localization to partition functions of vector and chiral multiplets on AdS 2 × T 2 , with and without a boundary: in both instances we classify normalizability and boundary conditions for gauge, matter and ghost fields. The index is twisted as the dynamical fields are coupled to a R-symmetry background 1-form with non-trivial exterior derivative and proportional to the spin connection. After regularization, the index is written in terms of elliptic gamma functions, reminiscent of four-dimensional holomorphic blocks, and crucially depends on the R-charge. [ABSTRACT FROM AUTHOR]

We study cooperative games in which some of the coalitions are not viable and in addition, there are externalities among the feasible coalitions. These games are called here restricted partition function form games. For this class of games, two extensions of the Shapley value are proposed and characterized. [ABSTRACT FROM AUTHOR]

We determine the order of magnitude of the variance of the Fibonacci partition function. The answer is different to the most naive guess. The proof involves a diophantine system and an inhomogeneous linear recurrence. For a video summary of this paper, please visit https://youtu.be/nTeO_6Chqbo. [ABSTRACT FROM AUTHOR]

An algorithm for obtaining the Chaundy-Bullard identity for a vector partition function with weight that uses computer algebra methods is proposed. To automate this process in Maple, an algorithm was developed and implemented that calculates the values of the vector partition function with weight by finding non-negative solutions of systems of linear Diophantine equations that are used to form the identities involved. The algorithm's input data is represented by the set of integer vectors that form a pointed lattice cone and by some point from this cone, and the Chaundy-Bullard identity for the vector partition function with weight is its output. The code involved is stored in the depository and is ready-to-use. An example demonstrating the algorithm's operation is given. [ABSTRACT FROM AUTHOR]

The study investigates the combination of the Coulomb potential with itself (standard Coulombic potential) under the nonrelativistic wave equation. The energy equation and the corresponding unnormalized radial wave function are obtained using the parametric Nikiforov–Uvarov method. This is achieved by applying a Green–Aldrich approximation scheme to the centrifugal term. The resulting energy equation is utilized to calculate the partition function, from which thermodynamic properties such as mean energy, specific heat capacity, entropy, and free energy are derived. Numerical results are generated for the standard Coulombic potential and its special cases, including Coulomb potential with negative potential strength and Coulomb potential with positive potential strength. The study reveals that the system's energy is fully bounded. Notably, the two special cases, representing Coulomb–Coulomb potentials with positive and negative potential strengths, yield equal results when the strengths are equal but opposite in sign. The thermodynamic properties align with existing literature but exhibit some unique behaviors. [ABSTRACT FROM AUTHOR]

Denote by τ k (n) , ω (n) and μ 2 (n) the number of representations of n as a product of k natural numbers, the number of distinct prime factors of n and the characteristic function of the square-free integers, respectively. Let [ t ] be the integral part of real number t. For f = ω , 2 ω , μ 2 , τ k , we prove that ∑ n ≤ x f x n = x ∑ d ≥ 1 f (d) d (d + 1) + O (x f + ) for x → ∞ , where ω = 5 3 1 1 0 , 2 ω = 9 1 9 , μ 2 = 2 5 , τ k = 5 k − 1 1 0 k − 1 and > 0 is an arbitrarily small positive number. These improve the corresponding results of Bordellès. [ABSTRACT FROM AUTHOR]

In this note, we present some results on the convergence of Nekrasov partition functions as power series in the instanton counting parameter. We focus on U(N) N = 2 gauge theories in four dimensions with matter in the adjoint and in the fundamental representations of the gauge group, respectively, and find rigorous lower bounds for the convergence radius in the two cases: if the theory is conformal, then the series has at least a finite radius of convergence, while if it is asymptotically free it has infinite radius of convergence. Via AGT correspondence, this implies that the related irregular conformal blocks of W N algebrae admit a power expansion in the modulus converging in the whole plane. By specifying to the SU(2) case, we apply our results to analyze the convergence properties of the corresponding Painlevé τ -functions. [ABSTRACT FROM AUTHOR]

In part 1, we formally defined important physical concepts in statistical thermodynamics that undergird internal state variable (ISV) theory such as configurational subsystems (e.g., individual grains or phases), constrained local equilibrium, and thermally activated dislocation reactions in the context of crystal plasticity. The primal importance of the Gibbs free energy barrier to dislocation reactions within each subsystem was emphasized since the enthalpy barriers are affected by local constraint and resulting long-range and short-range athermal internal stresses acting within subsystems. In this work, we formally apply Gibbsian thermodynamics up to the saddle point of pending dislocation barrier reactions. The partition function based on reaction probability serves as the statistical mechanics basis for the change of Gibbs free energy that drives pending ensemble reactions; it is employed to define both the changes of the thermal entropy and configurational entropy of pending reactions; the latter enumerates reactions not only within subsystems, but also over permutations of subsystems, consistent with a multiscale hierarchy. Intrinsic entropy produced via post-reaction dynamic rearrangement and glide is of purely thermally dissipative character, being coupled to the thermal bath via dispersive phonon dynamics, and is distinguished from the entropy change of pending reactions. Building on the important concept of degree of correlation of thermally activated dislocation processes both within each subsystem and across the ensemble of subsystems introduced in part 1, we argue that nonequilibrium trajectories progressively trend toward increased correlation of enthalpy barriers across subsystems of the ensemble by virtue of internal stress redistribution among hard (unfavorable for extended dislocation reactions) and soft (more favorable) subsystems. The degree of correlation is a many-body concept involving populations of dislocations within and among various configurational subsystems. The present statistical thermodynamics framework invokes the constrained local equilibrium approach that fully respects heterogeneity of subsystems and distributions of barrier strengths, in common with ISV theory. However, literature forms of ISV theories are almost universally of reduced-order character to reduce complexity. Accordingly, reduced-order representations of ISV theory are presented for fully correlated conditions, as in standard representations of the hardening laws and flow kinetics of crystal plasticity, along with potential variations relevant to decorrelated behavior, including transients induced by unloading or changes in direction of the external applied stress. The origin of ensemble kinematic hardening with multiple back stress components due to interactions of hard and soft subsystems emerges naturally. [ABSTRACT FROM AUTHOR]

Indium (In) is a critical element for electronics and catalysis industries and a volatile metal during planet accretion. Indium isotopes can be used to study cosmochemical and geochemical processes, but no equilibrium indium isotope fractionation factor is available, which restricts our knowledge of indium enrichment and incorporation during geological processes. Here, we investigate the reduced partition function ratios (103 lnβ) of 115In/113In in indium-bearing minerals using first-principles calculations. The results show that 103 lnβ decreases in the following sequence of dzhalindite > laforetite > roquesite > cadmoindite > Ag-Sn-In-doped sphalerite ≈ Cu-In-doped sphalerite ≈ Cu-Sn-In-doped sphalerite > yixunite > indite > damiaoite > native indium. We found that chemical composition may affect indium isotope fractionation factor in indium-doped sphalerite with Zn/In from 4 to 80 and indium alloys by changing the length of indium bonds. Furthermore, the chemical composition is not only related to the bond length and coordination number (CN) of the target element but also to the electronegativity of other doped elements, which can influence equilibrium indium isotope fractionation. The variation in 103 lnβ of indium-doped sphalerites and independent minerals predicts measurable isotopic differences between indium-bearing minerals. The equilibrium indium isotope fractionation factors calculated in this study provide important guides for the potential applications of indium isotopes in geological processes. [ABSTRACT FROM AUTHOR]