Related papers: Nonequivalent ensembles and metastability
Classical and multiscale non-equilibrium thermodynamics have different histories and different objectives. In this Note we explain the differences and review some topics in which the multiscale viewpoint of mesoscopic time evolution of…
Relation between natural nonequilibrium steady states of Ruelle and MacLennan-Zubarev ensembles is discussed for a system consisting of $M$ infinitely extended systems coupled with a small system. And a characterization of quasistatic…
I discuss the effects of fermionic condensation in systems of constant density of states. I show that the condensation leads to a correction of the chemical potential and of the Fermi distribution in canonical Fermi systems at low…
The canonical and grand-canonical ensembles are two usual marginal cases for ultracold Bose gases, but real collections of experimental runs commonly have intermediate properties. Here we study the continuum of intermediate cases, and look…
Here we first develop the thermodynamics of microcanonical phase transitions of first and second order in systems which are thermodynamically stable in the sense of van Hove. We show how both kinds of phase transitions can unambiguously be…
We analyze the general relation between canonical and grand canonical ensembles in the thermodynamic limit. We begin our discussion by deriving, with an alternative approach, some standard results first obtained by Kac and coworkers in the…
Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions.…
Two examples of Microcanonical Potts models, 2-dimensional nearest neighbor and mean field, are considered via exact enumeration of states and analytical asymptotic methods. In the interval of energies corresponding to a first order phase…
The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the…
We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple…
We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…
For quantum systems that are weakly coupled to a much 'bigger' environment, thermalization of possibly far from equilibrium initial ensembles is demonstrated: for sufficiently large times, the ensemble is for all practical purposes…
We illustrate a novel characterization of nonequivalent statistical mechanical ensembles using the mean-field Blume-Emery-Griffiths (BEG) model as a test model. The novel characterization takes effect at the level of the microcanonical and…
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
In the context of nuclear physics Pratt recently investigated noninteracting Fermi systems described by the microcanonical and canonical ensemble. As will be shown his discussion of the model of equally spaced levels contains a flaw and a…
Construction of a nonlinear higher-order thermo-hydrodynamics, including correlations, in the framework of a Generalized Nonequilibrium Statistical Grand-Canonical Ensemble is presented. In that way it is provided a particular formalism for…
We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of…