Free energy functional for nonequilibrium systems: an exactly solvable case

We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size N, the probability of any macroscopic density profile rho(x) is exp[-NF([rho])]; F thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for F is a nonlocal functional of rho, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.     

Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations

We elaborate and compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for a purely dissipative isothermal driven diffusive system under steady state conditions. The fluctuation dissipation relations of both approaches play an important role for a detailed comparison. The nonequilibrium Helmholtz free energies introduced in these two approaches differ as a result of boundary conditions. A Fokker-Planck equation derived by projection operator techniques properly reproduces long range fluctuations in nonequilibrium steady states and offers the most promising possibility to describe the physically relevant fluctuations around macroscopic averages for time-dependent nonequilibrium systems.     

Hysteresis in one-dimensional reaction-diffusion systems

We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics in one dimension. The steady state exhibits a phase with broken ergodicity and hysteresis which has no analog in systems investigated previously. We identify the main dynamical mode, viz., the random motion of a shock in an effective potential, which provides a unified framework for understanding phase coexistence as well as ergodicity breaking. This picture also leads to the exact phase diagram of the system.     

Einstein Relation for Nonequilibrium Steady States

The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds if the steady state satisfies detailed balance. More generally, we consider nonequilibrium steady states where detailed balance does not hold and show how a generalisation of the Einstein relation may be derived in certain cases. In particular, for the asymmetric simple exclusion process and a driven diffusive dimer model, the external perturbation creates and annihilates particles thus breaking the particle conservation of the unperturbed model.     

Fast-ionic-conductor behavior of driven lattice-gas models

We discuss driven diffusive lattice-gas systems as a model for fast ionic conductors, derive associated hydrodynamic equations and expressions for transport coefficients, and compare mean-field theory, Monte Carlo results and experimental observations. The comparison between model and real behaviours helps to understand some properties of those materials which seem to be characterized by the occurrence of nonequilibrium steady states and phase transitions. In particular, our study suggests the existence in Nature of a novel (nonequilibrium) universality class.     

Inequivalence of dynamical ensembles in a generalized driven diffusive lattice gas

We generalize the driven diffusive lattice gas model by using a combination of Kawasaki and Glauber dynamics. We find via Monte Carlo simulations and perturbation studies that the simplest possible generalization of the equivalence of the canonical and grand-canonical ensembles, which holds in equilibrium, does not apply for this class of nonequilibrium systems.     

Bulk-driven nonequilibrium phase transitions in a mesoscopic ring

We study a periodic one-dimensional exclusion process composed of a driven and a diffusive part. In a mesoscopic limit where both dynamics compete we identify bulk-driven phase transitions. We employ mean-field theory complemented by Monte Carlo simulations to characterize the emerging nonequilibrium steady states. Monte Carlo simulations reveal interesting correlation effects that we explain phenomenologically.     

Excess Entropy Production in Quantum System: Quantum Master Equation Approach

For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry–Sinitsyn–Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by \(\ln \breve{\rho }_0\) and \(\rho _0\) where \(\rho _0\) is the instantaneous steady state of the QME and \(\breve{\rho }_0\) is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.     

Generalized clausius inequality for nonequilibrium quantum processes

We show that the nonequilibrium entropy production for a driven quantum system is larger than the Bures length, the geometric distance between its actual state and the corresponding equilibrium state. This universal lower bound generalizes the Clausius inequality to arbitrary nonequilibrium processes beyond linear response. We further derive a fundamental upper bound for the quantum entropy production rate and discuss its connection to the Bremermann-Bekenstein bound.     

Optical properties of nonequilibrium low-dimensional systems

The optical properties of low-dimensional carrier systems ("quantum wire" type) driven away from equilibrium are studied. The frequency and wave-vector-dependent dielectric function of a quasi-one-dimensional electron system under the action of an exciting external pumping source is derived. The optical responses of the system are obtained in terms of its nonequilibrium thermodynamic state, the latter characterized resorting to a nonequilibrium statistical ensemble formalism.     

Reaction and concentration dependent diffusion model

We study the formation of patterns in the genuinely nonlinear reaction diffusion model equation u(t)+2a(u(2))(x) = (u(2))(xx)+F(x,u), where u may be viewed as an amplitude of a thermal wave in plasma or density of a biological species and F = u(1-u) or F = q(x)u(l), l = 0,2. We provide a transformation which maps the model into a purely diffusive process free of its interacting part and its intrinsic temporal and spatial scales. The well known attractors of the diffusive process enable us to completely characterize the emerging patterns which, depending on F and initialization, may be a semicompact, or a compact, traveling wave or a nontrivial equilibrium.     

The theory of shot noise in the space-charge-limited diffusive conduction regime

As is well known, fluctuations from a stable stationary nonequilibrium state are described by the linearized inhomogeneous Boltzmann-Langevin equation. The stationary state itself can be described by the nonlinear Boltzmann equation. The ways of its linearization sometimes seem to be not unique. We argue that there is actually a unique way to obtain a linear equation for the fluctuations. As an example, we consider an analytical theory of nonequilibrium shot noise in a diffusive conductor under the space-charge-limited regime. Our approach is compared to that in [11]. We find some difference between the present theory and the approach in [11] and discuss a possible origin of the difference. We believe that it is related to the fundamentals of the theory of fluctuation phenomena in a nonequilibrium electron gas.     

A maximum entropy mean field method for driven diffusive systems

We introduce a method of generating systematic mean field (MF) approximations for the nonequilibrium steady state of ferromagnetic Ising driven diffusive systems (DDS), based on the maximum entropy principle due to Jaynes. In the phase coexistence region, MF approximations to the master equation do not provide a closed system of equations in the MF variables. This can be traced to the conservation of the order parameter by the stochastic dynamics. Our maximum entropy mean field (MEMF) approximation method is applicable to high temperatures as well to the low-temperature phase coexistence region. It is based on a derivation of a generalized variational free energy from the maximum entropy principle, with the MF evolution equations playing the role of constraints. In the phase coexistence region this free energy is nonconvex and is interpreted by means of a Maxwell construction. We use a pair-level variant of the MEMF approximation to calculate quantities of interest for the ferro-magnetic Ising DDS on a square lattice. Results of calculations with several different choices of transition rates satisfying local detailed balance are discussed and compared with those obtained by other methods.     

A Diffusive System Driven by a Battery or by a Smoothly Varying Field

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit the long range pair correlation functions of the system driven by a battery are very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models.     

High-temperature expansion for nonequilibrium steady states in driven lattice gases

We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas, the "Ising model" for nonequilibrium physics. We represent the steady state as P(eta) alpha e(-betaH(eta)-psi(eta)) and evaluate the lowest order contribution to the nonequilibrium effective interaction psi(eta). We see that, in dimensions d > or = 2, all models with nonsingular transition rates yield the same summable psi(eta), suggesting the possibility of describing the state as a Gibbs state similar to equilibrium. The models with the Metropolis rule show exceptional behavior.     

Nonequilibrium mechanics and dynamics of motor-activated gels

The mechanics of cells is strongly affected by molecular motors that generate forces in the cellular cytoskeleton. We develop a model for cytoskeletal networks driven out of equilibrium by molecular motors exerting transient contractile stresses. Using this model we show how motor activity can dramatically increase the network's bulk elastic moduli. We also show how motor binding kinetics naturally leads to enhanced low-frequency stress fluctuations that result in nonequilibrium diffusive motion within an elastic network, as seen in recent in vitro and in vivo experiments.     

Optical properties of III-nitrides in electric fields

The influence of intermediate to high electric fields on the optical properties of direct-gap strongly-polar III-Nitrides is characterized. It is manifested through the dependence on the electric field of the nonequilibrium thermodynamic state of the system, which is characterized by a nonequilibrium effective temperature (quasi-temperature), quasi-chemical potentials and drift velocities of the excited carriers driven away from equilibrium, and the quasi-temperatures of the phonons in the different branches. In particular, we analyze the processes of absorption and luminescence, and a field-dependent Roosbroeck-Shockley relation is derived. It is shown that it is possible to measure the carriers’ drift velocity and quasi-temperature, in the steady state or with ultrafast time resolution, resorting to luminescence together with Raman scattering experiments.