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We study linear response theory and entropic fluctuations of finite dimensional non-equilibrium Repeated Interaction Systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different values, we prove analogs of the Green–Kubo fluctuation–dissipation formula and Onsager reciprocity relations on energy flux observables. Then we prove a Large Deviation Principle, or Fluctuation Theorem, and a Central Limit Theorem on the full counting statistics of entropy fluxes. We consider two types of non-equilibrium RIS: either the temperatures of the probes are deterministic and arrive in a cyclic way, or the temperatures of the probes are described by a sequence of i.i.d. random variables with uniform distribution over a finite set. [ABSTRACT FROM AUTHOR]

This article presents an idealized mathematical model of the cerebral cortex, focusing on the dynamical interaction of neurons. The author proposes a network architecture more consistent with neuroanatomy than in previous studies, borrows ideas from nonequilibrium statistical mechanics and calls attention to the fact that the brain is a large and complex dynamical system. The ideas proposed are illustrated with a realistic model of the visual cortex. [ABSTRACT FROM AUTHOR]

In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in Sasamoto and Wadati (Phys Rev E 58:4181–4190, 1998), Barraquand and Corwin (Probab Theory Relat Fields 167(3–4):1057–1116, 2017) and Povolotsky (J Phys A 46(46):465205, 2013) in the context of KPZ universality class. We show that they may be mapped onto an integrable sl (2) Heisenberg spin chain whose Hamiltonian density in the bulk has been already studied in the AdS/CFT and the integrable system literature. Using the quantum inverse scattering method, we study various new aspects, in particular we identify boundary terms, modeling reservoirs in non-equilibrium statistical mechanics models, for which the spin chain (and thus also the stochastic process) continues to be integrable. We also show how the construction of a "dual model" of probability theory is possible and useful. The fluctuating hydrodynamics of our stochastic model corresponds to the semiclassical evolution of a string that derives from correlation functions of local gauge invariant operators of N = 4 super Yang–Mills theory (SYM), in imaginary-time. As any stochastic system, it has a supersymmetric completion that encodes for the thermal equilibrium theorems: we show that in this case it is equivalent to the sl (2 | 1) superstring that has been derived directly from N = 4 SYM. [ABSTRACT FROM AUTHOR]

We study the structure of stationary non-equilibrium states for interacting particle systems from a microscopic viewpoint. In particular we discuss two different discrete geometric constructions. We apply both of them to determine non reversible transition rates corresponding to a fixed invariant measure. The first one uses the equivalence of this problem with the construction of divergence free flows on the transition graph. Since divergence free flows are characterized by cyclic decompositions we can generate families of models from elementary cycles on the configuration space. The second construction is a functional discrete Hodge decomposition for translational covariant discrete vector fields. According to this, for example, the instantaneous current of any interacting particle system on a finite torus can be canonically decomposed in a gradient part, a circulation term and an harmonic component. All the three components are associated with functions on the configuration space. This decomposition is unique and constructive. The stationary condition can be interpreted as an orthogonality condition with respect to an harmonic discrete vector field and we use this decomposition to construct models having a fixed invariant measure. [ABSTRACT FROM AUTHOR]

We present the reduced dynamics of a bead in a Rouse chain which is submerged in a bath containing a driving agent that renders it out-of-equilibrium. We first review the generalized Langevin equation of the middle bead in an equilibrated bath. Thereafter, we introduce two driving forces. Firstly, we add a constant force that is applied to the first bead of the chain. We investigate how the generalized Langevin equation changes due to this perturbation for which the system evolves towards a steady state after some time. Secondly, we consider the case of stochastic active forces which will drive the system to a nonequilibrium state. Including these active forces results in an extra contribution to the second fluctuation-dissipation relation. The form of this active contribution is analysed for the specific case of Gaussian, exponentially correlated active forces. We also discuss the resulting rich dynamics of the middle bead in which various regimes of normal diffusion, subdiffusion and superdiffusion can be present. [ABSTRACT FROM AUTHOR]

The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent nontrivial diffusivity matrices, as we show with an application to an experiment of two trapped and hydrodynamically coupled colloids, one of which is subject to an external random forcing that mimics an effective temperature. The nonequilibrium susceptibility of the energy to a variation of this driving is an example of our formulation, which improves an earlier version, as it does not depend on the time-discretization of the stochastic dynamics. This scheme holds for generic systems with additive noise and can be easily implemented numerically, thanks to matrix operations. [ABSTRACT FROM AUTHOR]

In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory (Freidlin and Wentzell, Random perturbations of dynamical systems, ). In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory (Bertini et al., , ), which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to $$1/\sqrt{N}$$ , where N is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter $$\lambda $$ , starting from a known quasi-potential for $$\lambda =0$$ . In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner (Stochastics 20:247-308, ; Stochastic differential systems, vol 96, pp 1-10, ). Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators (Prog Theoret Phys 75:1105-1110, []). This is one of few systems for which non-equilibrium free energies can be computed and analyzed in an effective way, at least perturbatively. [ABSTRACT FROM AUTHOR]

We consider a finite region of a d-dimensional lattice of nonlinear Hamiltonian rotators, where neighbouring rotators have opposite (alternated) spins and are coupled by a small potential of size $$\varepsilon ^a,\, a\ge 1/2$$ . We weakly stochastically perturb the system in such a way that each rotator interacts with its own stochastic thermostat with a force of order $$\varepsilon $$ . Then we introduce action-angle variables for the system of uncoupled rotators ( $$\varepsilon = 0$$ ) and note that the sum of actions over all nodes is conserved by the purely Hamiltonian dynamics of the system with $$\varepsilon >0$$ . We investigate the limiting (as $$\varepsilon \rightarrow 0$$ ) dynamics of actions for solutions of the $$\varepsilon $$ -perturbed system on time intervals of order $$\varepsilon ^{-1}$$ . It turns out that the limiting dynamics is governed by a certain autonomous (stochastic) equation for the vector of actions. This equation has a completely non-Hamiltonian nature. This is a consequence of the fact that the system of rotators with alternated spins do not have resonances of the first order. The $$\varepsilon $$ -perturbed system has a unique stationary measure $$\widetilde{\mu }^\varepsilon $$ and is mixing. Any limiting point of the family $$\{\widetilde{\mu }^\varepsilon \}$$ of stationary measures as $$\varepsilon \rightarrow 0$$ is an invariant measure of the system of uncoupled integrable rotators. There are plenty of such measures. However, it turns out that only one of them describes the limiting dynamics of the $$\varepsilon $$ -perturbed system: we prove that a limiting point of $$\{\widetilde{\mu }^\varepsilon \}$$ is unique, its projection to the space of actions is the unique stationary measure of the autonomous equation above, which turns out to be mixing, and its projection to the space of angles is the normalized Lebesque measure on the torus $$\mathbb {T}^N$$ . The results and convergences, which concern the behaviour of actions on long time intervals, are uniform in the number $$N$$ of rotators. Those, concerning the stationary measures, are uniform in $$N$$ in some natural cases. [ABSTRACT FROM AUTHOR]

We consider the dynamics of a freely movable wall of mass $$M$$ with one degree of freedom that separates a long tube into two regions, each of which is filled with rarefied gas particles of mass $$m$$ . The gases are initially prepared at equal pressure but different temperatures, and we assume that the pressure and temperature of gas particles before colliding with the wall are kept constant over time in each region. We elucidate the energetics of the setup on the basis of the local detailed balance condition, and then derive the expression for the heat transferred from each gas to the wall. Furthermore, by using the condition, we obtain the linear response formula for the steady velocity of the wall and steady energy flux through the wall. By using perturbation expansion in a small parameter $$\epsilon \equiv \sqrt{m/M}$$ , we calculate the steady velocity up to order $$\epsilon $$ . [ABSTRACT FROM AUTHOR]

We consider a class of mechanical particle systems with deterministic particle-disk interactions coupled to Gibbs heat reservoirs at possibly different temperatures. We show that there exists a unique (non-equilibrium) steady state. This steady state is mixing, but not exponentially mixing, and all initial distributions converge to it. In addition, for a class of initial distributions, the rates of converge to the steady state are sub-exponential. [ABSTRACT FROM AUTHOR]

The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback-Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems). [ABSTRACT FROM AUTHOR]

We propose an alternative method to compute the environmental entropy production of a classical underdamped nonequilibrium system, not necessarily in detailed balance, in a continuous phase space. It is based on the idea that the Hamiltonian orbits of the corresponding isolated system can be regarded as microstates and that entropy is generated in the environment whenever the system moves from one microstate to another. This approach has the advantage that it is not necessary to distinguish between even and odd-parity variables. We show that the method leads to a different expression for the differential entropy production along an infinitesimal stochastic path. However, when integrating over all possible paths the local entropy production turns out to be the same as in previous studies. This demonstrates that the differential entropy production in continuous phase space systems is not uniquely defined. [ABSTRACT FROM AUTHOR]

In scientific topics ranging from protein folding to the thermohaline ocean circulation, it is useful to model the effective macroscopic dynamics of complex systems as noise-driven motion in a potential landscape. In this paper we consider the estimation of such models from a collection of short non-equilibrium trajectories between two points in phase-space. We generalize a recently introduced spectral methodology for the estimation of diffusion processes from timeseries, so that it can be used for non-equilibrium data. This methodology makes use of the spectral properties (leading eigenvalue-eigenfunction pairs) of the Fokker-Planck operator associated with the diffusion process. It is well suited to infer stochastic differential equations that give effective, coarse-grained descriptions of multiscale systems. The generalization to the non-equilibrium situation is illustrated with numerical examples in which potentials and diffusion coefficients are estimated from ensembles of short trajectories. [ABSTRACT FROM AUTHOR]

We study nonequilibrium steady states of some 1-D mechanical models with N moving particles on a line segment connected to unequal heat baths. For a system in which particles move freely, exchanging energy as they collide with one another, we prove that the mean energy along the chain is constant and equal to $\frac{1}{2} \sqrt{T_{L}T_{R}}$ where T and T are the temperatures of the two baths. We then consider systems in which particles are trapped, i.e., each confined to its designated interval in the phase space, but these intervals overlap to permit interaction of neighbors. For these systems, we show numerically that the system has well defined local temperatures and obeys Fourier's Law (with energy-dependent conductivity) provided we vary the masses randomly to enable the repartitioning of energy. Dynamical systems issues that arise in this study are discussed though their resolution is beyond reach. [ABSTRACT FROM AUTHOR]

We review the theoretical underpinning of nonequilibrium umbrella sampling. We provide its historical context and show how it relates to other important results in nonequilibrium statistical mechanics. Its relationships to the generalised Yamada-Kawasaki distribution function is explored. A new functional version of the Crooks Fluctuation Theorem is also presented. [ABSTRACT FROM AUTHOR]

Reconstructing free energy profiles is an important problem in bimolecular reactions, protein folding or allosteric conformational changes. Nonequilibrium trajectories are readily measured experimentally, but their statistical significance and relation to equilibrium system properties still call for rigorous methods of assessment and interpretation. Here we introduce methods to compute the equilibrium free energy profile of a given variable from a set of short nonequilibrium trajectories, obtained by externally driving a system out of equilibrium and subsequently observing its relaxation. This protocol is not suitable for the Jarzynski equality since the irreversible work on the system is instantaneous. Assuming that the variable of interest satisfies an overdamped Langevin equation, which is frequently used for modeling biomolecular processes, we show that the trajectories sample a nonequilibrium stationary distribution that can be calculated in closed form. This allows for the estimation of the free energy via an inversion procedure that is analogous to that used in equilibrium and bypasses more complicated path integral methods, which we derive for comparison. We generalize the inversion procedure to systems with a diffusion constant that depends on the reaction coordinate, as is the case in protein folding, as well as to protocols in which the trajectories are initiated at random points. Using only a statistical pool of tens of synthetic trajectories, we demonstrate the versatility of these methods by reconstructing double and multi-well potentials, as well as a proposed profile for the hydrophobic collapse of a protein. [ABSTRACT FROM AUTHOR]

The phenomenon of protein synthesis has been modeled in terms of totally asymmetric simple exclusion processes (TASEP) since 1968. In this article, we provide a tutorial of the biological and mathematical aspects of this approach. We also summarize several new results, concerned with limited resources in the cell and simple estimates for the current (protein production rate) of a TASEP with inhomogeneous hopping rates, reflecting the characteristics of real genes. [ABSTRACT FROM AUTHOR]

kinetic equation for the single particle distribution function in an open many-body system, when in far away from equilibrium conditions is derived in the context of a Non-Equilibrium Thermo-Statistics of ample scope. It consists of a generalization of traditional kinetic equations in that no restrictions are imposed on the characteristics of the nonequilibrium thermodynamic state of the system. This kinetic equation do contain some contributions that become relevant in systems with a nonlinear kinetics when driven sufficiently far from equilibrium (certain complex systems). Moreover, the handling of the kinetic equation in a multiple-moment approach provides a generalized nonlinear higher-order thermo-hydrodynamics. [ABSTRACT FROM AUTHOR]

We consider the asymmetric simple exclusion processes (ASEP) on a ring constrained to produce an atypically large flux, or an extreme activity. Using quantum free fermion techniques we find the time-dependent conditional transition probabilities and the exact dynamical structure function under such conditioned dynamics. In the thermodynamic limit we obtain the explicit scaling form. This gives a direct proof that the dynamical exponent in the extreme current regime is z=1 rather than the KPZ exponent z=3/2 which characterizes the ASEP in the regime of typical currents. Some of our results extend to the activity in the partially asymmetric simple exclusion process, including the symmetric case. [ABSTRACT FROM AUTHOR]

Five previously unknown inequalities relating equilibrium free energy differences and non-equilibrium work fluctuations are derived, and lucid path to derivation of many similar inequalities is presented. These results are based upon combined exploitation of the Jarzynski equality and the generalization of the scheme for producing uncertainty-type inequalities due to H. Weyl. The inequalities may possibly lead to better understanding of behavior of the equilibrium free-energy estimators from non-equilibrium experimental data in many important applications concerning biological, chemical, and physical molecular processes. [ABSTRACT FROM AUTHOR]

A simple spatially two-dimensional stochastic cellular automaton with asymmetric coupling and synchronous updating according to Glauber rates is considered. While detailed balance is violated it is still possible to compute analytically the stationary probability distribution by elementary means. The stationary distribution can be written as a canonical equilibrium distribution of a spin system on a triangular lattice with nearest neighbour coupling. Thus, the cellular automaton shows a nonequilibrium phase transition with Ising critical behaviour. [ABSTRACT FROM AUTHOR]

Thermostats models in space dimension d=1,2,3 for nonequilibrium statistical mechanics are considered and it is shown that, in the thermodynamic limit, the evolutions admit infinitely many constants of motion: namely the intensive observables. [ABSTRACT FROM AUTHOR]

The kinetics of phase separation or domain growth, subsequent to temperature quenches of binary mixtures from the one-phase region into the miscibility gap, still remains a challenging problem of nonequilibrium statistical mechanics. We have an incomplete understanding of many aspects of the growth of concentration inhomogeneities, including the effect of surfaces on this process, and the interplay with wetting phenomena and finite-size effects in thin films. In the present paper, an overview of the simulation approaches to this problem is given, with an emphasis on solutions of a diffusive Ginzburg-Landau model. We also discuss two recent alternative approaches: a local molecular field approximation to the Kawasaki spin exchange model on a lattice; and molecular dynamics simulations of a fluid binary Lennard-Jones mixture. A brief outlook to open questions is also given. [ABSTRACT FROM AUTHOR]

A two-dimensional atomistic realization of Schlögl’s second model for autocatalysis is implemented and studied on a square lattice as a prototypical nonequilibrium model with first-order transition. The model has no explicit symmetry and its phase transition can be viewed as the nonequilibrium counterpart of liquid-vapor phase separations. We show some familiar concepts from study of equilibrium systems need to be modified. Most importantly, phase coexistence can be a generic feature of the model, occurring over a finite region of the parameter space. The first-order transition becomes continuous as a temperature-like variable increases. The associated critical behavior is studied through Monte Carlo simulations and shown to be in the two-dimensional Ising universality class. However, some common expectations regarding finite-size corrections and fractal properties of geometric clusters for equilibrium systems seems to be inapplicable. [ABSTRACT FROM AUTHOR]

Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the phase space contraction rate and the currents have been linked to its derivatives with respect to the parameters measuring the forcing intensities. In some instances Green–Kubo formulae, hence Onsager reciprocity, have been related to the fluctuation theorem. However, mainly when dissipation takes place at the boundary (as in gases or liquids in contact with thermostats), phase space contraction may be independent on some of the forcing parameters or, even in absence of forcing, phase space contraction may not vanish: then the relation with the fluctuation theorem does not seem to apply. On the other hand phase space contraction can be altered by changing the metric on phase space: here this ambiguity is discussed and employed to show that the relation between the fluctuation theorem and Green–Kubo formulae can be extended and is, by far, more general. [ABSTRACT FROM AUTHOR]

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the “degree of nonequilibrium”, and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order. [ABSTRACT FROM AUTHOR]

Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first evidence of the validity of these integral relations for the linear and the second harmonic response for the perturbed Lorenz 63 system, by showing that numerical simulations agree up to high degree of accuracy with the theoretical predictions. Some new theoretical results, showing how to derive asymptotic behaviors and how to obtain recursively harmonic generation susceptibilities for general observables, are also presented. Our findings confirm the conceptual validity of the nonlinear response theory, suggest that the theory can be extended for more general non equilibrium steady state systems, and shed new light on the applicability of very general tools, based only upon the principle of causality, for diagnosing the behavior of perturbed chaotic systems and reconstructing their output signals, in situations where the fluctuation-dissipation relation is not of great help. [ABSTRACT FROM AUTHOR]

We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nosé-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in (D.J. Searles, et al., J. Stat. Phys. 128:1337, 2007), for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate Λ and of the dissipation function Ω, a similar relaxation regime at shorter averaging times is found. The quantity Ω satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity Λ appears to begin a monotonic convergence after such times. This is consistent with the fact that Ω and Λ differ by a total time derivative, and that the tails of the probability distribution function of Λ are Gaussian. [ABSTRACT FROM AUTHOR]

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system [ABSTRACT FROM AUTHOR]

We study the kinetic theory of driven and undriven granular gases, taking into account both translational and rotational degrees of freedom. We obtain the high-energy tail of the stationary bivariate energy distribution, depending on the total energy E and the ratio $x=\sqrt{E_{w}/E}$ of rotational energy E w to total energy. Extremely energetic particles have a unique and well-defined distribution f( x) which has several remarkable features: x is not uniformly distributed as in molecular gases; f( x) is not smooth but has multiple singularities. The latter behavior is sensitive to material properties such as the collision parameters, the moment of inertia and the collision rate. Interestingly, there are preferred ratios of rotational-to-total energy. In general, f( x) is strongly correlated with energy and the deviations from a uniform distribution grow with energy. We also solve for the energy distribution of freely cooling Maxwell Molecules and find qualitatively similar behavior. [ABSTRACT FROM AUTHOR]

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work. [ABSTRACT FROM AUTHOR]

We perform a simulation with the aim of checking the existence of a well defined stationary state for a two dimensional system of driven hard disks when energy dissipation takes place at the system boundaries and no bulk impurities are present. [ABSTRACT FROM AUTHOR]

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green’s function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen. [ABSTRACT FROM AUTHOR]

This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.] where we have proven the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes in thermally driven quantum open systems. In this note we extend the derivation of the Green-Kubo formula to heat and charge fluxes and discuss some other generalizations of the model and results of [V. Jakšić Y. Ogata and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.]. [ABSTRACT FROM AUTHOR]

The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention and can lead to apparent inconsistencies. In particular there are several cases that have been considered in the literature in which singularities are built in the models: for instance when among the forces there are Lennard-Jones potentials (which are infinite in the origin) and the constraints imposed on the system do not forbid arbitrarily close approach to the singularity even though the average kinetic energy is bounded. The situation is well understood in certain special cases in which the system is subject to Gaussian noise; here the treatment of rather general singular systems is considered and the predictions of the chaotic hypothesis for such situations are derived. The main conclusion is that the chaotic hypothesis is perfectly adequate to describe the singular physical systems we consider, ıe deterministic systems with thermostat forces acting according to Gauss' principle for the constraint of constant total kinetic energy (“isokinetic Gaussian thermostats”), close and far from equilibrium. Near equilibrium it even predicts a fluctuation relation which, in deterministic cases with more general thermostat forces (ıe not necessarily of Gaussian isokinetic nature), extends recent relations obtained in situations in which the thermostatting forces satisfy Gauss' principle. This relation agrees, where expected, with the fluctuation theorem for perfectly chaotic systems. The results are compared with some recent works in the literature. [ABSTRACT FROM AUTHOR]

We present a Monte Carlo study of the high-temperature phase of the two-dimensional driven lattice gas at infinite driving field. We define a finite-volume correlation length, verify that this definition has a good infinite-volume limit independent of the lattice geometry, and study its finite-size-scaling behavior. The results for the correlation length are in good agreement with the predictions based on the field theory proposed by Janssen, Schmittmann, Leung, and Cardy. The theoretical predictions for the susceptibility and the magnetization are also well verified. We show that the transverse Binder parameter vanishes at the critical point in all dimensions d⩾2 and discuss how such result should be expected in the theory of Janssen et al. in spite of the existence of a dangerously irrelevant operator. Our results confirm the Gaussian nature of the transverse excitations. [ABSTRACT FROM AUTHOR]

The study of low density, ultracold atomic Fermi gases is a promising avenue to understand fermion superfluidity from first principles. One technique currently used to bring Fermi gases in the degenerate regime is sympathetic cooling through a reservoir made of an ultracold Bose gas. We discuss a proposal for trapping and cooling of two-species Fermi–Bose mixtures into optical dipole traps made from combinations of laser beams having two different wavelengths. In these bichromatic traps it is possible, by a proper choice of the relative laser powers, to selectively trap the two species in such a way that fermions experience a stronger confinement than bosons. As a consequence, a deep Fermi degeneracy can be reached having at the same time a softer degenerate regime for the Bose gas. This leads to an increase in the sympathetic cooling efficiency and allows for higher precision thermometry of the Fermi–Bose mixture. [ABSTRACT FROM AUTHOR]

Features physicist Giovanni Jona-Lasinio who is being honored by friends, students, and colleagues at the occasion of his 70th birthday with articles featured in the "Journal of Statistical Physics." Jona-Lasinio's work on elementary particles physics, critical phenomena, probability theory, quantum mechanics, history of science, and nonequilibrium statistical mechanics; Character; Scientific personality; Introduction of the concept of effective action in quantum field theory; Studies in statistical mechanics; Work on a general theory of dynamical fluctuations for stationary nonequilibrium states; Study on the phenomenon of strong instability of the tunneling effect in quantum mechanics.

We study the heat transport in systems of coupled oscillators driven out of equilibrium by Gaussian heat baths. We illustrate with a few examples that such systems can exhibit “strange” transport phenomena. In particular, circulation of heat flux may appear in the steady state of a system of three oscillators only. This indicates that the direction of the heat fluxes can in general not be “guessed” from the temperatures of the heat baths. Although we primarily consider harmonic couplings between the oscillators, we explain why this strange behavior persists under weak anharmonic perturbations. [ABSTRACT FROM AUTHOR]

We study the non-equilibrium statistical mechanics of the two-sided XY chain. We start from an initial state in which the left and right part of the lattice, $\{\backslash Bbb\; Z\}\_\{\{\backslash rm\; L\}\}=\backslash \{x\backslash in\; \{\backslash Bbb\; Z\}\backslash mid\; x\; \backslash lt\; -M\backslash \},\backslash qquad\; \{\backslash Bbb\; Z\}\_\{\{\backslash rm\; R\}\}=\backslash \{x\backslash in\; \{\backslash Bbb\; Z\}\backslash mid\; x\; \backslash gt\; M\backslash \},$ are at inverse temperatures βL and βR. Using a simple scattering theoretic analysis, we construct the unique non-equilibrium steady state (NESS). This state depends on βL and βR, but not on the choice of the decoupling parameter M. We prove that in the non-equilibrium case, βL≠βR, this state has strictly positive entropy production. [ABSTRACT FROM AUTHOR]

We consider the quasi-deterministic behavior of systems with a large number, n, of deterministically interacting constituents. This work extends the results of a previous paper [ J. Statist. Phys. 99:1225–1249 (2000)] to include vector-valued observables on interacting systems. The approach used here, however, differs markedly in that a level-1 large deviation principle (LDP) on joint observables, rather than a level-2 LDP on empirical distributions, is employed. As before, we seek a mapping ψ t on the set of (possibly vector-valued) macrostates such that, when the macrostate is given to be a0 at time zero, the macrostate at time t is ψ t( a0) with a probability approaching one as n tends to infinity. We show that such a map exists and derives from a generalized dynamic free energy function, provided the latter is everywhere well defined, finite, and differentiable. We discuss some general properties of ψ t relevant to issues of irreversibility and end with an example of a simple interacting lattice, for which an exact macroscopic solution is obtained. [ABSTRACT FROM AUTHOR]

A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle distribution function and the mean interaction energy are treated as independent nonequilibrium state parameters. The density operator method is used to derive a kinetic equation in second-order non-Markovian Born approximation and an evolution equation for the nonequilibrium quasi-temperature which is thermodynamically conjugated to the mean interaction energy. The kinetic equation contains a correlation contribution which exactly cancels the collision term in thermal equilibrium and ensures the energy conservation in nonequilibrium states. Explicit expressions for the entropy production in the non-Markovian regime and the time-dependent correlation energy are obtained. [ABSTRACT FROM AUTHOR]

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large- n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as n→∞ to a value ψt( y) given explicitly in terms of a canonical expectation. Some general features of the graph of ψt( y) versus t are examined, particularly in regard to continuity, symmetry, and convergence. [ABSTRACT FROM AUTHOR]

The evolution of the distribution function of a dynamical system governed by a general two-dimensional area-preserving iterative map is studied by the methods of nonequilibrium statistical mechanics. A closed, non-Markovian master equation determines the angle-averaged distribution function (the “density profile”). The complementary, angle-dependent part (“the fluctuations”) is expressed as a non-Markovian functional of the density profile. Whenever there exist two widely separated intrinsic time scales, the master equation can be markovianized, yielding an asymptotic kinetic equation. The general theory is applied to the standard map in the diffusive regime, i.e., for large stochasticity parameter and large scale length. The non-Markovian master equation can be written and solved analytically in this approximation. The two characteristic time scales are exhibited. This permits the thorough study of the evolution of the density profile, its tendency toward the Markovian approximation, and eventually toward a diffusive Gaussian packet. The evolution of the fluctuations is also described in detail. The various relaxation processes are governed asymptotically by a single diffusion coefficient, which is calculated analytically. This model appears as a testing bench for the study of kinetic equations. The various previous approaches to this problem are reviewed and critically discussed. [ABSTRACT FROM AUTHOR]

We present a quantum system composed of infinitely many particles, subject to a nonquadratic Hamiltonian, for which it is possible to investigate the long time behavior of the dynamics and its ergodic properties. We do so both for the KMS states and for a large class of locally normal invariant states, whose very existence is already of some interest. [ABSTRACT FROM AUTHOR]

Nonequilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the transient and steady-state forms of the fluctuation theorem. In the case of planar Poiseuille flow, we find that the transient form, valid for all times, converges to the steady-state predictions on microscopic time scales. Further, we find that the time of convergence for the two theorems coincides with the time required for satisfaction of the asymptotic steady-state fluctuation theorem. [ABSTRACT FROM AUTHOR]