24 research outputs found
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
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
Macroscopic current fluctuations in stochastic lattice gases
We study current fluctuations in lattice gases in the macroscopic limit
extending the dynamic approach to density fluctuations developed in previous
articles. More precisely, we derive large deviation estimates for the
space--time fluctuations of the empirical current which include the previous
results. Large time asymptotic estimates for the fluctuations of the time
average of the current, recently established by Bodineau and Derrida, can be
derived in a more general setting. There are models where we have to modify
their estimates and some explicit examples are introduced.Comment: 4 pages, LaTeX, Changed conten
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
On the long range correlations of thermodynamic systems out of equilibrium
Experiments show that macroscopic systems in a stationary nonequilibrium
state exhibit long range correlations of the local thermodynamic variables. In
previous papers we proposed a Hamilton-Jacobi equation for the nonequilibrium
free energy as a basic principle of nonequilibrium thermodynamics. We show here
how an equation for the two point correlations can be derived from the
Hamilton-Jacobi equation for arbitrary transport coefficients for dynamics with
both external fields and boundary reservoirs. In contrast with fluctuating
hydrodynamics, this approach can be used to derive equations for correlations
of any order. Generically, the solutions of the equation for the correlation
functions are non-trivial and show that long range correlations are indeed a
common feature of nonequilibrium systems. Finally, we establish a criterion to
determine whether the local thermodynamic variables are positively or
negatively correlated in terms of properties of the transport coefficients.Comment: 4 page
Large deviations of the empirical current in interacting particle systems
We study current fluctuations in lattice gases in the hydrodynamic scaling
limit. More precisely, we prove a large deviation principle for the empirical
current in the symmetric simple exclusion process with rate functional I. We
then estimate the asymptotic probability of a fluctuation of the average
current over a large time interval and show that the corresponding rate
function can be obtained by solving a variational problem for the functional I.
For the symmetric simple exclusion process the minimizer is time independent so
that this variational problem can be reduced to a time independent one. On the
other hand, for other models the minimizer is time dependent. This phenomenon
is naturally interpreted as a dynamical phase transition.Comment: 26 page
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
Stochastic interacting particle systems out of equilibrium
This paper provides an introduction to some stochastic models of lattice
gases out of equilibrium and a discussion of results of various kinds obtained
in recent years. Although these models are different in their microscopic
features, a unified picture is emerging at the macroscopic level, applicable,
in our view, to real phenomena where diffusion is the dominating physical
mechanism. We rely mainly on an approach developed by the authors based on the
study of dynamical large fluctuations in stationary states of open systems. The
outcome of this approach is a theory connecting the non equilibrium
thermodynamics to the transport coefficients via a variational principle. This
leads ultimately to a functional derivative equation of Hamilton-Jacobi type
for the non equilibrium free energy in which local thermodynamic variables are
the independent arguments. In the first part of the paper we give a detailed
introduction to the microscopic dynamics considered, while the second part,
devoted to the macroscopic properties, illustrates many consequences of the
Hamilton-Jacobi equation. In both parts several novelties are included.Comment: 36 page
Fluctuations in Stationary non Equilibrium States
In this paper we formulate a dynamical fluctuation theory for stationary non
equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic
regime and is verified explicitly in stochastic models of interacting
particles. In our theory a crucial role is played by the time reversed
dynamics. Our results include the modification of the Onsager-Machlup theory in
the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a
non equilibrium, non linear fluctuation dissipation relation valid for a wide
class of systems
Macroscopic fluctuations theory of aerogel dynamics
We consider the thermodynamic potential describing the macroscopic
fluctuation of the current and local energy of a general class of Hamiltonian
models including aerogels. We argue that this potential is neither analytic nor
strictly convex, a property that should be expected in general but missing from
models studied in the literature. This opens the possibility of describing in
terms of a thermodynamic potential non-equilibrium phase transitions in a
concrete physical context. This special behaviour of the thermodynamic
potential is caused by the fact that the energy current is carried by particles
which may have arbitrary low speed with sufficiently large probability.Comment: final versio