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We develop a formulation of global thermodynamics for equilibrium systems under the influence of gravity. The free energy for simple fluids is extended to include a dependence on $(T, V, N, mgL)$, where $L$ represents the vertical system length in the direction of gravity. A central idea in this formulation is to uniquely fix the reference point of the gravitational potential, ensuring a consistent thermodynamic framework. Using this framework, we derive the probability density of thermodynamic quantities, which allows us to define a variational function for determining equilibrium liquid-gas coexistence under gravity. The resulting free energy landscape, derived from the variational function, reveals the local stability of liquid-gas configurations. Specifically, the liquid phase resides at the lower portion of the system due to gravity, while the inverted configuration (with liquid on top) is also locally stable in this landscape. Furthermore, we characterize the transition between these liquid-gas configurations as a first-order phase transition using the thermodynamic free energy of $(T,V,N,mgL)$. Finally, we validate the predictions of global thermodynamics through molecular dynamics simulations, demonstrating the applicability and accuracy of the proposed framework., Comment: 42 pages, 17 figures

Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is much larger than $\Lambda$, the discrete model becomes the standard fluctuating hydrodynamics, where the phase coexistence condition is given by the local equilibrium thermodynamics. In contrast, when $\ell < \Lambda$, the most probable density profile is determined by a new variational principle, where the chemical potential at the interface is found to deviate from the equilibrium coexistence chemical potential. This means that metastable states at equilibrium stably appear near the interface as the influence of the particle current. The variational function derived in the theoretical analysis is also found to be equivalent to the variational function formulated in an extended framework of thermodynamics called global thermodynamics. Finally, the validity of the theoretical result is confirmed by numerical simulations., Comment: 29 pages, 8 figures. Revised version

We investigate phase coexistence in a weakly stochastic reaction-diffusion system without assuming a continuum description. Concretely, for $(2N+1)$ diffusion-coupled vessels in which a chemical reaction exhibiting bistability occurs, we derive a condition for the phase coexistence in the limit $N \to \infty$. We then find that the phase coexistence condition depends on the rate of hopping between neighboring vessels. The conditions in the high- and low-hopping-rate limits are expressed in terms of two different potentials which are determined from the chemical reaction model in a single vessel., Comment: 6 pages, 5 figures (Supplemental Material: 5 pages, 4 figures)

We study a liquid-gas coexistence system in a container under gravity with heat flow in the direction opposite to gravity. By molecular dynamics simulation, we find that the liquid buoys up and continues to float steadily. The height at which the liquid floats is determined by a dimensionless parameter related to the ratio of the temperature gradient to gravity. We confirm that supercooled gas remains stable above the liquid. We provide a phenomenological argument for explaining the phenomenon from a simple thermodynamic assumption., Comment: 5 pages + supplementary material

Continued advances in quantum technologies rely on producing nanometer-scale wires. Although several state-of-the-art nanolithographic technologies and bottom-up synthesis processes have been used to engineer such wires, critical challenges remain in growing uniform atomic-scale crystalline wires and constructing their network structures. Here we discover a simple method to fabricate atomic-scale wires with various arrangements, including stripes, X-, Y-junctions, and nanorings. Single-crystalline atomic-scale wires of a Mott insulator, whose band gap is comparable to those of wide-gap semiconductors, are spontaneously grown on graphite substrates \DEL{and epitaxial monolayer graphene on SiC }by pulsed-laser deposition. These wires are one-unit-cell-thick and have an exact width of two- and four-unit-cells (1.4 and 2.8\,nm) and lengths up to a few $\mu m$. We show that the non-equilibrium reaction-diffusion processes may play an essential role in atomic pattern formation. Our findings offer a new perspective on the non-equilibrium self-organization phenomena on an atomic scale, paving a unique way for the quantum architecture of nano-network.

The steady propagation of a $(d-1)$-dimensional planer interface in $d$-dimensional space is studied by analyzing mesoscopic non-conserved order parameter dynamics with two local minima under the influence of thermal noise. In this analysis, an entropic force generating interface propagation is formulated using a perturbation method. It is found that the entropic force singularly depends on an ultraviolet cut-off when $d \ge 2$. The theoretical calculation is confirmed by numerical simulations with $d=2$. The result means that an experimental measurement of the entropic force provides an estimation of the microscopic cut-off of the mesoscopic description., Comment: 16 pages, 10 figures

We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed limits on the self-averaging of observables. In equilibrium, the bound takes the form of a tradeoff relation between the long- and short-time fluctuations of an observable. Out of equilibrium, the tradeoff can be violated, leading to an acceleration of self-averaging. We relate this violation to the steady-state entropy production rate, as well as the geometric structure of the irreversible currents, giving rise to two complementary speed limits. One of these can be formulated as a lower estimate on the entropy production from the measurement of time-symmetric observables. Using an illustrating example, we show the intricate behavior of the correlation time out of equilibrium for different classes of observables and how this can be used to partially infer dissipation even if no time-reversal symmetry breaking can be observed in the trajectories of the observable., Comment: 16 pages, 2 figures

In this paper, we prove the existence of a phase transition of parallelizability in the assembly of one-dimensional chains. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable/unparallelizable transition is then identified by the non-analytic change in the parallel efficiency from a positive value to zero. By evaluating the parallel efficiency on each side of the transition point, we show the existence of a phase transition in this system., Comment: This paper has been withdrawn by the authors. This paper has been superseded by arXiv:2302.00909 (merged from arXiv:2302.00909 and arXiv:2302.00914)

We propose a phase transition on the feasibility of efficient parallel assembly. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable/unparallelizable transition is then identified by the non-analytic change in the parallel efficiency from a positive value to zero. We present two analyzable models to demonstrate this phase transition in the limit of infinite system size., Comment: 11 pages, 12 figures

The local equilibrium thermodynamics is a basic assumption of macroscopic descriptions of the out of equilibrium dynamics for Hamiltonian systems. We numerically analyze the Hamiltonian Potts model in two dimensions to study the violation of the assumption for phase coexistence in heat conduction. We observe that the temperature of the interface between ordered and disordered states deviates from the equilibrium transition temperature, indicating that metastable states at equilibrium are stabilized by the influence of a heat flux. We also find that the deviation is described by the formula proposed in an extended framework of the thermodynamics., Comment: 20 pages, 10 figures

When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness., Comment: 6 pages, 4 figures (Supplemental Material: 11 pages, 8 figures)

For small thermodynamic systems in contact with a heat bath, we determine the free energy by imposing the following two conditions. First, the quasi-static work in any configuration change is equal to the free energy difference. Second, the temperature dependence of the free energy satisfies the Gibbs-Helmholtz relation. We find that these prerequisites uniquely lead to the free energy of a classical system consisting of $N$-interacting identical particles, up to an additive constant proportional to $N$. The free energy thus determined contains the Gibbs factorial $N!$ in addition to the phase space integration of the Gibbs-Boltzmann factor. The key step in the derivation is to construct a quasi-static decomposition of small thermodynamic systems., Comment: 11 pages, 2 figures

For a generic overdamped Langevin dynamics driven out of equilibrium by both time-dependent and nonconservative forces, the entropy production rate can be decomposed into two positive terms, termed excess and housekeeping entropy. However, this decomposition is not unique: There are two distinct decompositions, one due to Hatano and Sasa, the other one due to Maes and Neto\v{c}ny. Here, we establish the connection between these two decompositions and provide a simple, geometric interpretation. We show that this leads to a decomposition of the entropy production rate into three positive terms, which we call excess, housekeeping and coupling part, respectively. The coupling part characterizes the interplay between the time-dependent and nonconservative forces. We also derive thermodynamic uncertainty relations for the excess and housekeeping entropy in both the Hatano-Sasa and Maes-Neto\v{c}ny-decomposition and show that all quantities obey integral fluctuation theorems. We illustrate the decomposition into three terms using a solvable example of a dragged particle in a nonconservative force field., Comment: 26 pages, 7 figures

It is a fundamental problem how the universal concept of classical chaos emerges from the microscopic description of quantum mechanics. We here study standard classical chaos in a framework of quantum mechanics. In particular, we design a quantum lattice system that exactly simulates classical chaos after an appropriate continuum limit, which is called the "Hamiltonian equation limit". The key concept of our analysis is an entanglement entropy defined by dividing the lattice into many blocks of equal size and tracing out the degrees of freedom within each block. We refer to this entropy as the "interscale entanglement entropy" because it measures the amount of entanglement between the microscopic degrees of freedom within each block and the macroscopic degrees of freedom that define the large-scale structure of the wavefunction. By numerically simulating a quantum lattice system corresponding to the Hamiltonian of the kicked rotor, we find that the long-time average of the interscale entanglement entropy becomes positive only when chaos emerges in the Hamiltonian equation limit, and the growth rate of the entropy in the initial stage is proportional to that of the coarse-grained Gibbs entropy of the corresponding classical system., Comment: 12 pages, 8 figures

The maximum entropy principle determines the values of thermodynamic variables in thermally isolated equilibrium systems. This paper extends the principle to a variational principle that applies to liquid-gas coexistence in heat conduction. We show the uniqueness of the extension under the assumption that the variational principle and the fundamental thermodynamic relation are simultaneously extended in the linear response regime with the total energy fixed. Using the extended variational principle, we calculate the thermodynamic quantities in this steady state and find that the temperature of the liquid-gas interface deviates from the equilibrium transition temperature, which should be verified in experiments.

We introduce two properties, macroscopic mixing and transitive mixing, to represent the macroscopic stability of time evolution of Gibbs measures. We claim that these are fundamental properties of macroscopic systems that exhibit relaxation to an equilibrium state. As an illustration, we show that a simple mechanical system on a lattice possesses these two properties.

We present a simple model describing the assembly and disassembly of heteropolymers consisting of two types of monomers $A$ and $B$. We prove that no matter how we manipulate the concentrations of $A$ and $B$, it takes longer than the exponential function of $d$ to synthesize a fixed amount of the desired heteropolymer, where $d$ is the number of $A$-$B$ connections. We also prove the decomposition time is linear for chain length $n$. When $d$ is proportional to $n$, synthesis and destruction have an exponential asymmetry. Our findings may facilitate research on the more general asymmetry of operational hardness., Comment: 5 pages, 3 figures

When a stable phase is adjacent to a metastable phase with a planar interface, the stable phase grows. We propose a stochastic lattice model describing the phase growth accompanying heat diffusion. The model is based on an energy-conserving Potts model with a kinetic energy term defined on a two-dimensional lattice, where each site is sparse-randomly connected in one direction and local in the other direction. For this model, we calculate the stable and metastable phases exactly using statistical mechanics. Performing numerical simulations, we measure the displacement of the interface $R(t)$. We observe the scaling relation $R(t)=L_x \bar{\mathcal{R}} (Dt/L_x^2)$, where $D$ is the thermal diffusion constant and $L_x$ is the system size between the two heat baths. The scaling function $\bar{\mathcal{R}}(z)$ shows $\bar{\mathcal{R}}(z) \simeq z^{0.5}$ for $z \ll z_c$ and $\bar{\mathcal{R}}(z) \simeq z^{\alpha}$ for $z \gg z_c$, where the cross-over value $z_c$ and exponent $\alpha$ depend on the temperatures of the baths, and $0.5\le\alpha\le 1$. We then confirm that a deterministic phase-field model exhibits the same scaling relation. Moreover, numerical simulations of the phase-field model show that the cross-over value $\bar{\mathcal{R}}(z_c)$ approaches zero when the stable phase becomes neutral., Comment: 11pages,24 figures

Two qualitatively different ways of driving a physical system out of equilibrium, time-dependent and non-conservative forcing, are reflected by the decomposition of the system's entropy production into excess and housekeeping parts. We show that the difference between these two types of driving gives rise to a geometric formulation in terms of two orthogonal contributions to the currents in the system. This geometric picture in a natural way leads to variational expressions for both the excess and housekeeping entropy, which allow calculating both contributions independently from the trajectory data of the system. We demonstrate this by calculating the excess and housekeeping entropy of a particle in a time-dependent, tilted periodic potential., Comment: 7 pages, 2 figures

We study the two-dimensional surface long-range order in a non-equilibrium steady state under shear flow using the three-dimensional conserved $O(N)$ model. Whereas the correlation on the surface is enhanced by increasing interactions within the surface, the long-range order cannot be realized at equilibrium because of divergent thermal fluctuations associated with the low dimensionality of the surface. Here, the shear flow is applied parallel to the surface, on which the flow is set to zero. Despite the shear flow not affecting the order parameter on the surface directly, the fluctuations at the surface are strongly suppressed by the flow away from the surface, leading to the surface long-range order. We demonstrate these results through an exact analysis in the large-$N$ limit, where non-linear fluctuations are self-consistently treated., Comment: 17 pages, 9 figures

We propose a modified XY model in which cascade transfer emerges from spatially local interactions, where the spin corresponds to the "velocity" of a turbulent field. For this model, we theoretically calculate the scale-to-scale energy flux and the equal time correlation function in $d$ dimensions. The result indicates an inverse energy cascade with the non-Kolmogorov energy spectrum proportional to $k^{-3}$. We also numerically confirm the result for the cases $d=2$ and $d=3$. We thus conclude that the cascade transfer in our model represents a different universality class from standard fluid turbulence., Comment: 6 pages, 2 figures (+ supplemental material 3 pages, 8 figures). In ver. 2, the presentation has been revised substantially; In ver. 3, minor revisions are made

We discuss how to use correlations between different physical observables to improve recently obtained thermodynamics bounds, notably the fluctuation-response inequality (FRI) and the thermodynamic uncertainty relation (TUR). We show that increasing the number of measured observables will always produce a tighter bound. This tighter bound becomes particularly useful if one of the observables is a conserved quantity, whose expectation is invariant under a given perturbation of the system. For the case of the TUR, we show that this applies to any function of the state of the system. The resulting correlation-TUR takes into account the correlations between a current and a non-current observable, thereby tightening the TUR. We demonstrate our finding on a model of the $\text{F}_1$-ATPase molecular motor, a Markov jump model consisting of two rings and transport through a two-dimensional channel. We find that the correlation-TUR is significantly tighter than the TUR and can be close to an equality even far from equilibrium., Comment: 18 pages, 7 figures

When a stable ordered phase and a metastable disordered phase are separated by a flat interface, the metastable state changes to the stable state through the propagation of the interface. For cases in which latent heat is generated, the interface displacement during some time interval is proportional to the square root of the time interval when the extent of supercooling is less than a certain value. We demonstrate this behavior by deriving a perturbative solution for a propagating interface in the phase field model. We calculate the leading-order contribution explicitly, and find that the interface temperature deviates from the equilibrium transition temperature in proportion to the interface velocity., Comment: 8 pages, 2 figures

The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium., Comment: 5 + 3 pages

We investigate a quite strong turbulence in a supercritical fluid near a gas-liquid critical point. Specifically, we consider a case in which the Kolmogorov scale is much smaller than the equilibrium correlation length $\xi$. Although equilibrium critical fluctuations are destroyed by turbulence, $\xi$ still provides a crossover length scale between two types of energy cascade. At scales much larger than $\xi$, the Richardson cascade becomes dominant, whereas at scales much smaller than $\xi$, another type of cascade, which we call the van der Waals cascade, is induced by density fluctuations. Experimental conditions required to observe the van der Waals cascade are also discussed., Comment: 18 pages, 2 figures. Minor revisions are made in ver. 2. arXiv admin note: text overlap with arXiv:2009.11057

We theoretically and numerically investigate a two-dimensional O(2) model where an order parameter is convected by shear flow. We show that a long-range phase order emerges in two dimensions as a result of anomalous suppression of phase fluctuations by the shear flow. Furthermore, we use the finite-size scaling theory to demonstrate that a phase transition to the long-range ordered state from the disordered state is second order. At a transition point far from equilibrium, the critical exponents turn out to be close to the mean-field value for equilibrium systems., Comment: 21 pages, 14 figures

We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous time-reversal allows us to derive a tighter version of the thermodynamic uncertainty relation (TUR) involving observables evaluated relative to their local mean value. Moreover, the family of dynamics realizing the continuous time-reversal contains an equilibrium dynamics halfway between the time-forward and time-reversed dynamics. We show that this equilibrium dynamics, together with an appropriate choice of the observable, turns the inequality in the TUR into an equality. We demonstrate our findings for the example of a particle diffusing in a tilted periodic potential., Comment: 18 pages, 2 figures

We study fluctuating dynamics of a freely movable piston that separates an infinite cylinder into two regions filled with ideal gas particles at the same pressure but different temperatures. To investigate statistical properties of the time-averaged velocity of the piston in the long-time limit, we perturbatively calculate the large deviation function of the time-averaged velocity. Then, we derive an infinite number of effective Langevin equations yielding the same large deviation function as in the original model. Finally, we provide two possibilities for uniquely determining the form of the effective model., Comment: 9 pages

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK) like formula for the bare transport coefficients is presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system., Comment: 6+13 pages, 6 figures

We perform equilibrium molecular dynamics simulations for nanoscale fluids confined between two parallel walls and investigate how the autocorrelation function of force acting on one wall is related to the slip length. We demonstrate that for atomically smooth surfaces, the autocorrelation function is accurately described by linearized fluctuating hydrodynamics (LFH). Excellent agreement between the simulation and the LFH solution is found over a wide range of scales, specifically, from the time scale of fluid relaxation even to that of molecular motion. Fitting the simulation data yields a reasonable estimation of the slip length. We show that LFH provides a starting point for examining the relationship between the slip length and the force fluctuations., Comment: 16 pages, 8 figures

We study the thermodynamic entropy as a Noether invariant in a stochastic process. Following the Onsager theory, we consider the Langevin equation for a thermodynamic variable in a thermally isolated system. By analyzing the Martin-Siggia-Rose-Janssen-de Dominicis action of the Langevin equation, we find that this action possesses a continuous symmetry in quasi-static processes, which leads to the thermodynamic entropy as the Noether invariant for the symmetry., Comment: 12 pages, 2 figures

We propose a stochastic order parameter equation for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a non-equilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in non-equilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a super-heated ordered (super-cooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in [N. Nakagawa and S.-i. Sasa, Liquid-gas transitions in steady heat conduction, Phys. Rev. Lett. {\bf 119}, 260602, (2017).], Comment: 30 pages, 13 figures; In ver.2, the presentation has been substantially revised. 31 pages, 14 figures

We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of thermodynamics holds, which we call "global thermodynamics" for heat conduction systems. Associated with this global thermodynamics, we formulate a variational principle for determining thermodynamic properties of the liquid-gas phase coexistence in heat conduction, which corresponds to the natural extension of the Maxwell construction for equilibrium systems. We quantitatively predict that the temperature of the liquid-gas interface deviates from the equilibrium transition temperature. This result indicates that a super-cooled gas stably appears near the interface., Comment: 59 pages, 20 figures

Emergence of deterministic and irreversible macroscopic behavior from deterministic and reversible microscopic dynamics is understood as a result of the law of large numbers. In this paper, we prove on the basis of the theory of algorithmic randomness that Martin-L\"of random initial microstates satisfy an irreversible macroscopic law in the Kac infinite chain model. We find that the time-reversed state of a random state is not random as well as violates the macroscopic law., Comment: 21 pages

We investigate a thermally isolated quantum many-body system with an external control represented by a step protocol of a parameter. The propagator at each step of the parameter change is described by thermodynamic quantities under some assumptions. For the time evolution of such systems, we formulate a path integral over the trajectories in the thermodynamic state space. In particular, for quasi-static operations, we derive an effective action of the thermodynamic entropy and its canonically conjugate variable. Then, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant in quantum mechanics., Comment: 13 pages. This provides a new formulation for the result discussed in arXiv:1611.07268 which has been withdrawn

We provide general derivations of the partial slip boundary condition from microscopic dynamics and linearized fluctuating hydrodynamics. The derivations are based on the assumption of separation of scales between microscopic behavior, such as collision of particles, and macroscopic behavior, such as relaxation of fluid to global equilibrium. The derivations lead to several statistical mechanical expressions of the slip length, which are classified into two types. The expression in the first type is given as a local transport coefficient, which is related to the linear response theory that describes the relaxation process of the fluid. The second type is related to the linear response theory that describes the non-equilibrium steady state and the slip length is given as combination of global transport coefficients, which are dependent on macroscopic lengths such as a system size. Our derivations clarify that the separation of scales must be seriously considered in order to distinguish the expressions belonging to two types. Based on these linear response theories, we organize the relationship among the statistical mechanical expressions of the slip length suggested in previous studies., Comment: 42 pages, 5 figures

We provide a method for calculating time-averaged stress fluctuations on surfaces in a viscous incompressible fluid at equilibrium. We assume that (i) the time-averaged fluctuating stress is balanced in equilibrium at each position and that (ii) the time-averaged fluctuating stress obeys a Gaussian distribution on the restricted configuration space given by (i). Using these assumptions with the Green-Kubo formula for the viscosity, we can derive the large deviation function of the time-averaged fluctuating stress. Then, using the saddle-point method for the large deviation function, we obtain the time-averaged surface stress fluctuations. As an example, for a fluid between two parallel plates, we study the time-averaged shear/normal stress fluctuations per unit area on the top plate at equilibrium. We show that the surface shear/normal stress fluctuations are inversely proportional to the distance between the plates., Comment: 9 pages

We study boundary conditions applied to the macroscopic dynamics of Newtonian liquids from the view of microscopic particle systems. We assume the existence of microscopic boundary conditions that are uniquely determined from a microscopic description of the fluid and the wall. By using molecular dynamical simulations, we examine a possible form of the microscopic boundary conditions. In the macroscopic limit, we may introduce a scaled velocity field by ignoring the higher order terms in the velocity field that is calculated from the microscopic boundary condition and standard fluid mechanics. We define macroscopic boundary conditions as the boundary conditions that are imposed on the scaled velocity field. The macroscopic boundary conditions contain a few phenomenological parameters for an amount of slip, which are related to a functional form of the given microscopic boundary condition. By considering two macroscopic limits of the non-equilibrium steady state, we propose two different frameworks for determining macroscopic boundary conditions., Comment: 21 pages, 9 figures

We reply to the Comment by Singha and Barma on our Letter "Replica symmetry breaking in trajectories of a driven Brownian particle"., Comment: 2 pages, 2 figures

We study the Bose--Einstein condensation in a tight-binding model with a hopping rate enhanced only on a surface. We show that this model exhibits two different critical phenomena depending on whether the hopping rate on the surface $t_s$ exceeds the critical value $5t/4$, where $t$ is the hopping rate in the bulk. For $t_s/t<5/4$, normal Bose--Einstein condensation occurs, while the Bose--Einstein condensation for $t_s/t\geq5/4$ is characterized by the spatial localization of the macroscopic number of particles at the surface. By exactly calculating the surface free energy, we show that for $t_s/t<5/4$, the singularity of the surface free energy stems from diverging the correlation length in the bulk, while for $t_s/t\geq5/4$, it is induced by the coupling effects between the bulk and surface., Comment: 34 pages, 4 figures

We present a new approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation-response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback-Leibler divergence between the probability densities describing the perturbed and unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady state particle transport, the differential mobility is bounded by the diffusivity. For a virtual perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality., Comment: 14 pages, 1 figure

We derive a bound on generalized currents for Langevin systems in terms of the total entropy production in the system and its environment. For overdamped dynamics, any generalized current is bounded by the total rate of entropy production. We show that this entropic bound on the magnitude of generalized currents imposes power-efficiency tradeoff relations for ratchets in contact with a heat bath: Maximum efficiency---Carnot efficiency for a Smoluchowski-Feynman ratchet and unity for a flashing or rocking ratchet---can only be reached at vanishing power output. For underdamped dynamics, while there may be reversible currents that are not bounded by the entropy production rate, we show that the output power and heat absorption rate are irreversible currents and thus obey the same bound. As a consequence, a power-efficiency tradeoff relation holds not only for underdamped ratchets but also for periodically driven heat engines. For weak driving, the bound results in additional constraints on the Onsager matrix beyond those imposed by the Second Law. Finally, we discuss the connection between heat and entropy in a non-thermal situation where the friction and noise intensity are state-dependent., Comment: 18 pages, 2 figures

We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through the momentum current. We show that although the two expectation values converge to the same equilibrium value in the thermodynamic limit, the variance of the mechanical pressure is in general greater than that of the pressure defined through the thermodynamic relation. We also present a condition for experimentally detecting the difference between them in an idealized measurement of momentum transfer., Comment: 9 pages

We derive a universal bound on generalized currents in Langevin systems in terms of the mean-square fluctuations of the current and the total entropy production. This bound generalizes a relation previously found by Barato et al. to arbitrary times and transient states. Using the bound, we define a new efficiency for stochastic transport, which measures how close a given system comes to saturating the bound. The existence of such a bounded efficiency implies that stochastic transport is unavoidably accompanied by a fluctuations and dissipation, which cannot be reduced arbitrarily. We apply the definition of transport efficiency to steady state particle transport and heat engines and show that the transport efficiency may approach unity at finite current, in contrast to the thermodynamic efficiency. Finally, we derive a bound on purely diffusive transport in terms of the Shannon entropy., Comment: 13 pages, 2 figures

We study liquid-gas transitions of heat conduction systems in contact with two heat baths under constant pressure in the linear response regime. On the basis of local equilibrium thermodynamics, we propose an equality with a global temperature, which determines the volume near the equilibrium liquid-gas transition. We find that the formation of the liquid-gas interface is accompanied by a discontinuous change in the volume when increasing the mean temperature of the baths. A super-cooled gas near the interface is observed as a stable steady state., Comment: 6 pages, 4 figures and 9 pages, 1 figure for supplemental material

We study a noisy Kuramoto-Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar-Parisi-Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation., Comment: 16pages, 8figures, Revised version as a full paper

We investigate a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. We formulate a path integral in terms of thermal pure states and derive an effective action for trajectories in a thermodynamic state space, where the entropy appears with its conjugate variable. In particular, for quasi-static operations, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant., Comment: 12 pages. Explanations have been added in ver.2, Introduction has been substantially revised in ver.3, Withdrawal because our new paper arXiv:1812.06375 provides a better formulation for the result of this paper

We present a theoretical framework to analyze the violation of fluctuation-response relation (FRR) for any observable from a finite Markov system with two well-separated time scales. We find that, generally for both slow and fast observables, a broad plateau exists in the intermediate frequency region, which contributes to a finite hidden entropy production. Assuming that non-equilibrium behavior arises only from coupling of slow and fast processes, we find that, at large observation time scae, the effective temperature for a slow observable deviates only slightly from the bath temperature, accompanied by an emerging well-defined effective potential landscape, while the deviation is significant for a fast observable. Our study also identifies a wider range of applicability of the Harada-Sasa equality in Markov jumping systems., Comment: 19 pages, 8 figures

We show that uncorrelated Gaussian noise, despite its paradigmatic association with thermal equilibrium, can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle in a periodic potential with an internal degree of freedom and a state-dependent friction, coupled to an equilibrium bath. Applying additional Gaussian white noise drives the system into a non-equilibrium steady state and causes a finite current if the potential is spatially asymmetric. We calculate the current explicitly in the three complementary limits. Since the particle current is driven solely by additive Gaussian white noise, this shows that the latter can potentially be exploited as a work resource to power small engines. By comparing the extracted power to the energy injection due to the noise, we find an expression for the efficiency of such an engine., Comment: 11 pages, 5 figures