Related papers: Equilibration and Thermalization of Classical Syst…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
Isolated quantum system in a pure state may be perceived as thermal if only substantially small fraction of all degrees of freedom is probed. We propose that in a chaotic quantum many-body system all states with sufficiently small energy…
We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the…
We derive the continuous canonical distribution only by requiring the extensivity of the mean energy and the multiplicative probabilistic composition rule. The derivation is independent of the thermodynamic limit and moreover it does not…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work,…
The properties of discrete nonlinear symmetries of integrable equations are investigated. These symmetries are shown to be canonical transformations. On the basis of the considered examples, it is concluded, that the densities of the…
A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. As an application, it is shown that this nonequilibrium…
We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal…
Post-exponential decay of the probability density of a quantum particle leaving a trap can be reproduced accurately, except for interference oscillations at the transition to the post-exponential regime, by means of an ensemble of classical…
Why is thermalisation a universal phenomenon? How does a quantum system reach thermodynamical equilibrium? These questions are not new, dating even from the very birth of quantum theory and have been the subject of a renewed interest over…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
In this article we investigate the long time behavior of solutions to a class of infinitely many master equations defined from transition rates that are suitable for the description of a quantum system approaching thermodynamical…
In this article it is shown that in a classical equilibrium canonical ensemble of molecules with $s$-body interaction full Gibbs distribution can be uniquely expressed in terms of a reduced s-particle distribution function. This means that…
It is well known that a system, S, weakly coupled to a heat bath, B, is described by the canonical ensemble when the composite, S+B, is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true both for…
We investigate the time evolution of a generic and finite isolated quantum many-body system starting from a pure quantum state. We find the kinematical general canonical principle proposed by Popescu-Short-Winter for statistical mechanics…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…