English
Related papers

Related papers: An entropy for groups of intermediate growth

200 papers

The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme…

Statistical Mechanics · Physics 2022-06-30 Cillian Cockrell , Ian J Ford

Let $G$ be a group acting properly by isometries and with a strongly contracting element on a geodesic metric space. Let $N$ be an infinite normal subgroup of $G$, and let $\delta_N$ and $\delta_G$ be the growth rates of $N$ and $G$ with…

Group Theory · Mathematics 2020-06-10 Goulnara N. Arzhantseva , Christopher H. Cashen

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

Physics and Society · Physics 2021-04-29 Felipe Xavier Costa , Pedro Pessoa

Chater and MacKay [CM] derived an entropy function of state for exchange economies satisfying a list of axioms, and showed that a change of state of a system of such economies is possible if and only if their total entropy does not…

Mathematical Physics · Physics 2025-10-03 Robert S MacKay

We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of…

Dynamical Systems · Mathematics 2023-06-22 Javier Correa , Enrique R. Pujals

The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…

Methodology · Statistics 2022-02-03 Madhur Mangalam , Damian G. Kelty-Stephen

During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…

Statistical Mechanics · Physics 2009-11-07 Michael Nauenberg

A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…

Data Analysis, Statistics and Probability · Physics 2007-05-23 S. S. Apostolov , Z. A. Mayzelis , O. V. Usatenko , V. A. Yampol'skii

Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…

General Relativity and Quantum Cosmology · Physics 2024-03-20 Soumya Chakrabarti

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium…

Statistical Mechanics · Physics 2014-03-26 Leo P. Kadanoff

We propose an entropic geometrical model of psycho-physical crowd dynamics (with dissipative crowd kinematics), using Feynman action-amplitude formalism that operates on three synergetic levels: macro, meso and micro. The intent is to…

Adaptation and Self-Organizing Systems · Physics 2008-11-27 Vladimir G. Ivancevic , Darryn J. Reid

We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a…

Quantum Physics · Physics 2008-01-23 O. J. E. Maroney

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…

Statistical Mechanics · Physics 2009-11-11 A. S. Parvan

Physical systems with non-reciprocal or dissipative forces evolve according to a generalization of Liouville's equation that accounts for the expansion and contraction of phase space volume. Here, we connect geometric descriptions of these…

Statistical Mechanics · Physics 2025-05-27 Mohamed Sahbani , Swetamber Das , Jason R. Green

Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…

Condensed Matter · Physics 2009-11-10 V. I. Yukalov

We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional $S_{BG}[p(x)]…

Statistical Mechanics · Physics 2017-11-08 Guiomar Ruiz , Ugur Tirnakli , Ernesto P. Borges , Constantino Tsallis

We apply a recent proposal to define "gravitational entropy" to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational…

General Relativity and Quantum Cosmology · Physics 2014-08-15 Roberto A. Sussman

In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…

Dynamical Systems · Mathematics 2019-09-24 Nelda Jaque , Bernardo San Martín

We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…

Statistical Mechanics · Physics 2009-11-07 Frank Zielen , Andreas Schadschneider

Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…

Quantum Physics · Physics 2015-09-11 Ariel Caticha