Related papers: Boltzmannian Equilibrium in Stochastic Systems
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…
Lecture notes on elements of nonequilibrium statistical mechanics: (1) a characterization of the nonequilibrium condition, largely by contrast to equilibrium; (2) a retelling of some of the great performances of the more distant past,…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
The first part of the paper is devoted to the foundations, that is the mathematical and physical justification, of equilibrium statistical mechanics. It is a pedagogical attempt, mostly based on Khinchin's presentation, which purpose is to…
We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…
We propose a new formulation of the fluctuating lattice Boltzmann equation that is consistent with both equilibrium statististical mechanics and fluctuating hydrodynamics. The formalism is based on a generalized lattice-gas model, with each…
In this chapter, we present a straightforward geometrical argument that in a certain way recalls us the equivalence between the canonical and the microcanonical ensembles in the thermodynamic limit for the particular context of physical…
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…
A survey of the approach to Statistical Mechanics following Boltzmann's theory of ensembles and ergodic hypothesis leading to chaoticity as a unifying principle of equilibrium and nonequilibrium Statistical Mechanics.
The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
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…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling--even if often this step is not made explicit--and any model has to neglect details while still being physically accurate.…
Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up…
As the quantification of metabolism, nonequilibrium steady states play a central role in living matter, but are beyond the purview of equilibrium statistical mechanics. Here we develop a fermionic theory of nonequilibrium steady states in…