Related papers: Boltzmannian Equilibrium in Stochastic Systems
Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual…
Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered. The relativistic mass distribution for…
The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff's diagram technique and the assumption on the system under consideration to possess a wide variety…
Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the…
A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local "quasi-equilibrium" state a non-hydrodynamic dynamical…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble, whereas canonical ones fail in the most interesting, mostly inhomogeneous, situations like phase separations or away from the thermodynamic…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…