Related papers: A lemma about molecular chaos
We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions (correlation errors) measuring the deviations in time from the statistical independence of…
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 present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
There is studied an infinite system of point entities in $\mathbb{R}^d$ which reproduce themselves and die, also due to competition. The system's states are probability measures on the space of configurations of entities. Their evolution is…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
The indeterministic character of physical laws is generally considered to be the most important consequence of quantum physics. A deterministic point of view, however, together with the possibility of well defined Hamiltonian trajectories,…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…
We study the kinetics of ballistic annihilation for a one-dimensional ideal gas with continuous velocity distribution. A dynamical scaling theory for the long time behavior of the system is derived. Its validity is supported by extensive…
The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach…
A chain of kinetic equations for non-equilibrium one-particle, two-particle and $ s $-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev…
We present a general analytic framework for the evolution of cosmic structure in multi-species dark matter models that simultaneously incorporates finite velocity dispersion and Poisson fluctuations. Our approach accommodates arbitrary…
Dynamical random walk of classical particle in thermodynamically equilibrium fluctuating medium, - Gaussian random potential field, - is considered in the framework of explicit stochastic representation of deterministic interactions. We…
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…
A fast and efficient numerical-analytical approach is proposed for description of complex behaviour in non-equilibrium ensembles in the BBGKY framework. We construct the multiscale representation for hierarchy of partition functions by…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…