Related papers: Ergodicity of some open systems with particle-disk…

We analyse certain degenerate infinite dimensional sub-elliptic generators, and obtain estimates on the long-time behaviour of the corresponding Markov semigroups that describe a certain model of heat conduction. In particular, we establish…

We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations. We apply three different tests for ergodicity: a direct method comparing the time average of a particle momentum and position…

Deterministic dynamical systems such as the baker maps are useful to shed light on some of the conditions verified by deterministic models in non-equilibrium statistical physics. We investigate a 2D dynamical system, enjoying a weak form of…

We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity…

Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn-Hilliard and Allen-Cahn…

Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…

We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical systems. Under quite general hypotheses, the free energy is shown to be almost upper-semicontinuous: some normalised component of a limit…

We study equilibrium states of an infinite system of interacting particles in a Euclidean space. The particles bear `unbounded' spins with a given symmetric a priori distribution. The interaction between the particles is pairwise and splits…

In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full…

We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analogues of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to possess a unique…

Using the gauge-gravity duality, we argue that for a certain class of out-of-equilibrium steady-state systems in contact with a thermal background at a given temperature, the macroscopic physics can be captured by an effective thermodynamic…

Reciprocal relations correlate fairly accurately a great variety of experimental results. Nevertheless, the concepts of statistical fluctuations, and microscopic reversibility - the bases of the accepted proof of the relations by Onsager -…

We revisit the dynamics of the one-dimensional self-gravitating sheets models. We show that homogeneous and non-homogeneous states have different ergodic properties. The former is non-ergodic and the one-particle distribution function has a…

This paper analyzes the ergodic hypothesis in the context of Boltzmann's late work in statistical mechanics, where Boltzmann lays the foundations for what is today known as the typicality account. I argue that, based on the concepts of…

Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…

A picture for thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations…

A detailed analysis of the adiabatic-piston problem reveals peculiar dynamical features that challenge the general belief that isolated systems necessarily reach a static equilibrium state. In particular, the fact that the piston behaves…

We design several examples of constrained, symmetric quantum circuit dynamics that generate non-equilibrium steady states. The qubit networks maintain local memory of the initial conditions and display inhomogeneous subsystem dynamics over…

We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…

Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation…