Related papers: Statistical Mechanical Foundations for Systems wit…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
We discuss the possibility of using generalized canonical distributions, i.e. using other factors than $\exp(-\beta E)$, in order to compute the equilibrium properties of physical systems. It will be show that some other choices can, in…
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space…
Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…
The established technique of eliminating upper or lower parameters in a general hypergeometric series is profitably exploited to create pathways among confluent hypergeometric functions, binomial functions, Bessel functions, and exponential…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…
Exponential families form the backbone of modern statistics and machine learning, but textbooks seldom derive them from first principles in an accessible way. Although minimal sufficiency and the principle of maximum entropy, originating in…
We show that within classical statistical mechanics it is possible to naturally derive power law distributions which are of Tsallis type. The only assumption is that microcanonical distributions have to be separable from of the total system…
It is argued that the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system having Tsallis entropy. So it should be respected by all exact calculations…
It is shown that power law phase space distributions describe marginally stable Gibbsian equilibria far from thermal equilibrium which are expected to occur in collisionless plasmas containing fully developed quasi-stationary turbulence.…
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 framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, thus simple models exhibiting some…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium…
We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…
A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\sum…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
In this paper we derive the canonical distribution as a stationary solution of the Liouville equation for the classical dissipative system. Dissipative classical systems can have stationary states look like canonical Gibbs distributions.…