Related papers: Axiomatic Tests for the Boltzmann Distribution
Difference Boltzmann Equation is derived in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors is used as the second…
Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states. They have been widely studied in the neural computing…
The relativistic Boltzmann equation for a single particle species generally implies a fixed, unchangeable equation of state that corresponds to that of an ideal gas. Real-world systems typically have more complicated equation of state which…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
We construct and explore a family of states for quantum systems in contact with two or more heath reservoirs. The reservoirs are described by equilibrium distributions. The interaction of each reservoir with the bulk of the system is…
We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio $\Theta$ of the diffusion constant to the differential mobility is not equal to the temperature of the environment (multiplied by the…
To obtain further insight on possible power law generalizations of Boltzmann equilibrium concepts, a stochastic collision model is investigated. We consider the dynamics of a tracer particle of mass $M$, undergoing elastic collisions with…
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling…
Starting with the fractal inspired distribution functions for Maxwell-Boltzmann, Bose-Einstein and Fermi systems, as reported by F. B\"{u}y\"{u}kkili\c{c} and D. Demirhan, we obtain the corresponding probability distributions and study…
The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is…
Classical-like formulas are given in order to evaluate thermal averages of observables belonging to a quantum nonlinear system with dissipation described by the Caldeira-Leggett model [Phys. Rev. Lett. 46, 211 (1981); Ann. Phys. (N.Y.) 149,…
A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle…
We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
In this work two systems are analyzed within the framework of the relativistic Boltzmann equation. One of them refers to a description of binary mixtures of electrons and protons and of electrons and photons subjected to external…
A novel formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small…
The probability distribution function for thermodynamics and econophysics is obtained by solving an equilibrium equation. This approach is different from the common one of optimizing the entropy of the system or obtaining the state of…