Related papers: Boltzmannian Equilibrium in Stochastic Systems
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
Within the description of stochastic differential equations it is argued that the existence of Boltzmann-Gibbs type distribution in economy is independent of the time reversal symmetry in econodynamics. Both power law and exponential…
We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much…
This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie-Bohm-Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
The theories of stochastic quantum mechanics and stochastic electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further previous work regarding the connection…
In this paper, we consider the volume enclosed by the microcanonical ensemble in phase space as a statistical ensemble. This can be interpreted as an intermediate image between the microcanonical and the canonical pictures. By maintaining…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…
This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role…
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…
New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key…
This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6.…
We consider the kinetic theory of dilute gases in the Boltzmann--Grad limit. We propose a new perspective based on a large deviation estimate for the probability of the empirical distribution dynamics. Assuming Boltzmann molecular chaos…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state…
Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…