Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an underlying microscopic dynamics: the only input required are transport coefficients as functions of thermodynamic variables, which are experimentally accessible. The basic postulates are local equilibrium which allows a hydrodynamic description of the evolution, the Einstein relation among the transport coefficients, and a variational principle defining the out of equilibrium free energy. Associated to the variational principle there is a Hamilton-Jacobi equation satisfied by the free energy, very useful for concrete calculations. Correlations over a macroscopic scale are, in our scheme, a generic property of nonequilibrium states. Correlation functions of any order can be calculated from the free energy functional which is generically a non local functional of thermodynamic variables. Special attention is given to the notion of equilibrium state from the standpoint of nonequilibrium.Comment: 21 page

Non equilibrium current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation $j$ of the empirical current with a rate functional \mc I (j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional \mc I . We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of \mc I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.Comment: 36 Pages, No figur

A nonequilibrium extension of the Clausius heat theorem

We generalize the Clausius (in)equality to overdamped mesoscopic and macroscopic diffusions in the presence of nonconservative forces. In contrast to previous frameworks, we use a decomposition scheme for heat which is based on an exact variant of the Minimum Entropy Production Principle as obtained from dynamical fluctuation theory. This new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium. The argument remains exactly intact for diffusing fields where the fields correspond to macroscopic profiles of interacting particles under hydrodynamic fluctuations. We also show that the change of Shannon entropy is related to the antisymmetric part under a modified time-reversal of the time-integrated entropy flux.Comment: 23 pages; v2: manuscript significantly extende

Quark fragmentation into vector and pseudoscalar mesons at LEP

Some data on the ratio of vector to vector + pseudoscalar mesons, V/(V+P), and the probability of helicity zero vector states, rho_00, are now available from LEP. A possible relation between these two quantities and their interpretation in terms of polarized fragmentation functions are discussed; numerical estimates are given for the relative occupancies of K and K*, D and D*, B and B* states.Comment: 5 pages, no figure

Lagrangian phase transitions in nonequilibrium thermodynamic systems

In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in nonequilibrium this is not necessarily the case. We show that in nonequilibrium a new type of singularities can appear that are interpreted as phase transitions. In particular, this phenomenon occurs for the one-dimensional boundary driven weakly asymmetric exclusion process when the drift due to the external field is opposite to the one due to the external reservoirs, and strong enough.Comment: 10 pages, 2 figure

Minimum dissipation principle in stationary non equilibrium states

We generalize to non equilibrium states Onsager's minimum dissipation principle. We also interpret this principle and some previous results in terms of optimal control theory. Entropy production plays the role of the cost necessary to drive the system to a prescribed macroscopic configuration

Quantitative analysis of Clausius inequality

In the context of driven diffusive systems, for thermodynamic transformations over a large but finite time window, we derive an expansion of the energy balance. In particular, we characterize the transformations which minimize the energy dissipation and describe the optimal correction to the quasi-static limit. Surprisingly, in the case of transformations between homogeneous equilibrium states of an ideal gas, the optimal transformation is a sequence of inhomogeneous equilibrium states.Comment: arXiv admin note: text overlap with arXiv:1404.646

Long range correlations and phase transition in non-equilibrium diffusive systems

We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the occurrence of a phase transition as they become singular when the system approaches the transition

Large deviation approach to non equilibrium processes in stochastic lattice gases

We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.Comment: Extended version of the lectures given by G. Jona-Lasinio at the 9th Brazilian school of Probability, August 200