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We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
The molecular dynamics lattice gas method maps a molecular dynamics simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method by taking a Boltzmann average…
We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including…
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…
The general relativistic notion of gravitational and inertial mass is discussed from the general viewpoint of the tidal forces implicit in the curvature and the Einstein field equations within ponderable matter. A simple yet rigorously…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
In this paper we present a new derivation of the $H$-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we…
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…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
Non-equilibrium systems have long-ranged spatial correlations even far away from critical points. This implies that the likelihoods of spatial steady state profiles of physical observables are nonlocal functionals. In this letter, it is…
We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability distribution is computed by first mapping…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
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…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…