Related papers: Multicanonical distribution: Statistical equilibri…
Equilibrium canonical distribution in statistical mechanics assumes weak system-bath coupling (SBC). In real physical situations this assumption can be invalid and equilibrium quantum statistics of the system may be non-canonical. By…
The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate…
We present a thermodynamic theory for a generic population of $M$ individuals distributed into $N$ groups (clusters). We construct the ensemble of all distributions with fixed $M$ and $N$, introduce a selection functional that embodies the…
A principle of hierarchical entropy maximization is proposed for generalized superstatistical systems, which are characterized by the existence of three levels of dynamics. If a generalized superstatistical system comprises a set of…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
We study the grand-canonical ensemble with a fluctuating number of degrees of freedom in the context of generalized thermostatistics. Several choices of grand-canonical entropy functional are considered. The ideal gas is taken as an…
A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…
We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
Two recently proposed expressions for the computation of the entropy in the microcanonical ensemble are compared, and their equivalence is proved. These expressions are valid for a certain class of statistical mechanics systems, that can be…
I propose a numerical simulation algorithm for statistical systems which combines a microcanonical transfer of energy with global changes in clusters of spins. The advantages of the cluster approach near a critical point augment the speed…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
Boltzmann's principle S(E,N,V...)=ln W(E,N,V...) allows the interpretation of Statistical Mechanics of a closed system as Pseudo-Riemannian geometry in the space of the conserved parameters E,N,V... (the conserved mechanical parameters in…
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 consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law…
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
Superstatistics [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a superposition of…
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…