Related papers: Statistical mechanics of interfaces
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
In this expository paper we give an overview of some statistical methods for the monitoring of social networks. We discuss the advantages and limitations of various methods as well as some relevant issues. One of our primary contributions…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
Choice models for populations of agents on graphs are studied in terms of statistical thermodynamics. Equations of state are derived and discussed for different connectivity schemes, utility approximations, and temperature and volume…
We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
We study the classical statistical mechanics of a phase-space curve. This unveils a mechanism that, via the associated entropic force, provides us with a simple realization of effects such as confinement, hard core, and asymptotic freedom.…
We present a review of data types and statistical methods often encountered in astronomy. The aim is to provide an introduction to statistical applications in astronomy for statisticians and computer scientists. We highlight the complex,…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
This is an overview of various aspects of the 6-vertex model in statistical mechanics and related models.
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
We review a study of the Internet traffic properties. We analyze under what conditions the reported results could be reproduced. Relations of results of passive measurements and those of modelling are also discussed. An example of the…
This is a lightning introduction to some modern techniques used in the study of the statistical properties of hyperbolic dynamical systems. The emphasis is not in presenting a comprehensive theory but rather in fleshing out the main ideas…