Related papers: Entropy and equilibria in competitive systems
The formal consideration of the concept of interaction in thermodynamic analysis makes it possible to deduce, in the broadest terms, new results related to the coevolution of interacting systems, irrespective of their distance from…
A fundamental problem in evolutionary ecology research is to explain how different species coexist in natural ecosystems. This question is directly related with species trophic competition. However, competition theory, based on the…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing…
Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic…
Within the Tsallis thermodynamics' framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is…
This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper we study the coexistence of competing species at the fixed point of population dynamic…
In his ninth memoir Clausius summarizes the two principles of thermodynamics as follows: "The whole mechanical theory of heat rests on two fundamental theorems: that of equivalence of heat and work, and that of equivalence of…
This article is a short version of a longer article to appear in Physics Reports (cond-mat/9708200). The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of…
We propose new results for the existence and uniqueness of a general nonparametric and nonseparable competitive equilibrium with substitutes. These results ensure the invertibility of a general competitive system. The existing literature…
Tsallis' non-extensive statistical mechanics is claimed to be the correct tool to describe the behaviour of low-dimensional dissipative maps at the edge of chaos. Indeed, many different approaches confirm that, for those systems, the…
We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy…
This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the…
In this work, we derive information-theoretic properties for a modified Tsallis entropy, hereinafter referred to as q-entropy. We introduce the notions of joint q-entropy, conditional q-entropy, relative q-entropy, conditional mutual…
The extension of thermodynamic principles to active matter remains a challenge due to the non-equilibrium nature inherent to active systems. In this study, we introduce a framework to assess entropy in our minimal macroscopic experiment…