# Dynamical ensembles in stationary states

@article{Gallavotti1995DynamicalEI, title={Dynamical ensembles in stationary states}, author={Giovanni Gallavotti and Ezechiel G D Cohen}, journal={Journal of Statistical Physics}, year={1995}, volume={80}, pages={931-970} }

We propose, as a generalization of an idea of Ruelle's to describe turbulent fluid flow, a chaotic hypothesis for reversible dissipative many-particle systems in nonequilibrium stationary states in general. This implies an extension of the zeroth law of thermodynamics to nonequilibrium states and it leads to the identification of a unique distribution μ describing the asymptotic properties of the time evolution of the system for initial data randomly chosen with respect to a uniform…

## 712 Citations

Heat and fluctuations from order to chaos

- Physics
- 2008

Abstract.The Heat theorem reveals the second law of
equilibrium Thermodynamics (i.e. existence of Entropy) as a
manifestation of a general property of Hamiltonian Mechanics and of
the Ergodic…

Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics

- Physics
- 1999

This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics. We adopt a new point of view which has emerged…

Fluctuations in two-dimensional reversibly damped turbulence

- Physics
- 1999

Gallavotti proposed an equivalence principle in hydrodynamics, which states that forced-damped fluids can be equally well represented by means of the Navier-Stokes equations and by means of…

Fluctuation Relations and Nonequilibrium Response for Chaotic Dissipative Dynamics

- Physics
- 2013

In a recent paper [Colangeli and Rondoni, Physica D 241:681, 2011] it was argued that the Fluctuation Relation for the phase space contraction rate Λ could suitably be extended to non-reversible…

Dynamical systems of eternal inflation: a possible solution to the problems of entropy, measure, observables and initial conditions

- Physics
- 2012

There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts…

Nonequilibrium Steady State Thermodynamics and Fluctuations for Stochastic Systems

- Physics
- 2008

Abstract
We use the work done on and the heat removed from a system to maintain it in a nonequilibrium steady state for a thermodynamic-like description of such a system as well as of its…

Stationary nonequilibrium states in boundary-driven Hamiltonian systems: Shear flow

- Physics
- 1997

We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by…

Fluctuation theorem for constrained equilibrium systems.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

Finite-time averages of the phase-space contraction rate have nontrivial fluctuations which are complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states and show that these fluctuations are distributed according to a Gaussian curve for long enough times.

## References

SHOWING 1-10 OF 62 REFERENCES

Steady-state electrical conduction in the periodic Lorentz gas

- Mathematics
- 1993

We study nonequilibrium steady states in the Lorentz gas of periodic scatterers when an electric external field is applied and the particle kinetic energy is held fixed by a “thermostat” constructed…

NONEQUILIBRIUM MOLECULAR DYNAMICS OF CLASSICAL FLUIDS

- Physics
- 1992

Nonequilibrium systems in thermodynamic steady states can be studied by computer simulation, and the calculated transport coefficients are in agreement with results obtained by equilibrium methods.…

Ergodic theory of chaos and strange attractors

- Physics
- 1985

Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the…

Stationary shear flow in boundary driven Hamiltonian systems.

- PhysicsPhysical review letters
- 1995

The average rates of phase space volume contraction and macroscopic entropy production are shown to be equal for stationary hydrodynamic shear flows, i.e. when the velocity distribution of particles incident on the walls is a local Maxwellian.

Dynamical Ensembles in Nonequilibrium Statistical Mechanics.

- PhysicsPhysical review letters
- 1995

This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.

Resolution of Loschmidt's paradox: The origin of irreversible behavior in reversible atomistic dynamics.

- PhysicsPhysical review letters
- 1987

Nosromane-bar mechanics provides a link between computer simulations of nonequilibrium processes and real-world experiments and shows that irreversible behavior consistent with the second law of thermodynamics arises from completely reversible microscopic motion.

Distribution of characteristic exponents in the thermodynamic limit

- Physics
- 1986

The existence of the thermodynamic limit for the spectrum of the Lyapunov characteristic exponents is numerically investigated for the Fermi-Pasta-Ulam p model. We show that the shape of the spectrum…

Probability of second law violations in shearing steady states.

- MathematicsPhysical review letters
- 1993

An expression for the probability of fluctuations in the shear stress of a fluid in a nonequilibrium steady state far from equilibrium is given and a formula for the ratio that, for a finite time, theShear stress reverse sign is violating the second law of thermodynamics.

Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties

- MathematicsErgodic Theory and Dynamical Systems
- 1992

Abstract We introduce a class of dynamical systems on a Riemannian manifold with singularities having attractors with strong hyperbolic behavior of trajectories. This class includes a number of…

Field-dependent conductivity and diffusion in a two-dimensional Lorentz gas

- Physics
- 1993

The conductivity and diffusion of a color-charged two-dimensional thermostatted Lorentz gas in a color field is studied by a variety of methods. In this gas, point particles move through a regular…