Related papers: The different paths to entropy

Building on work of Kontsevich, we introduce a definition of the entropy of a finite probability distribution in which the "probabilities" are integers modulo a prime p. The entropy, too, is an integer mod p. Entropy mod p is shown to be…

We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities ("charges") between two systems initialized in thermal states. Three common formulae…

I want to combine two hitherto largely independent research projects, scientific understanding and mechanistic explanations. Understanding is not only achieved by answering why-questions, that is, by providing scientific explanations, but…

Dunkel and Hilbert, "Consistent thermostatistics forbids negative absolute temperatures," Nature Physics, {\bf 10}, 67 (2014), and Hilbert, H\"anggi, and Dunkel, "Thermodynamic laws in isolated systems," Phys. Rev. E {\bf 90}, 062116 (2014)…

In a recent paper [Entropy 2020, 22(1), 17] C. Tsallis states that entropy -- as in Shannon's or Kullback-Leiber's definitions -- is inadequate to interpret black hole entropy and suggests that a new non-additive functional should take the…

Entropic forces have recently attracted considerable attention as ways to reformulate, retrodict, and perhaps even "explain'" classical Newtonian gravity from a rather specific thermodynamic perspective. In this article I point out that if…

The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the…

We analyze a gas of noninteracting fermions confined to a one-dimensional harmonic oscillator potential, with the aim of distinguishing between two proposed definitions of the thermodynamic entropy in the microcanonical ensemble, namely the…

For models with several time-dependent components generalized entropies can be defined. This is shown for the Bianchi type IX model. We first derive the Cardy-Verlinde formula under the assumption that the first law of thermodynamics is…

We give meaning to the first and second laws of thermodynamics in case of mesoscopic out-of-equilibrium systems which are driven by diffusion processes. The notion of the entropy production is analyzed. The role of the Helmholtz extremum…

A historical perspective is presented on thermodynamics from the pioneering contributions by Carnot and Clausius to recent advances on active matter. Non-equilibrium thermodynamics develops from the identification of the irreversible…

A simple and effective approach to thermodynamics is suggested, which solves the major difficulties in the traditional presentation of the subject. The internal energy is introduced from the behavior of deformable bodies, whereas the…

We define the notion of entropy for a cross section of an action of continuous amenable group and relate it to the entropy of the ambient action. As a result, we are able to answer a question of J.P. Thouvenot about completely positive…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…

The explanation of the apparent universality of thermodynamics points toward the extension of the usual conceptual background of the second law. Arguments are collected that a basic guiding idea of stability of thermodynamic equilibrium…

Assuming the hypothesis of the entropic nature of gravity, we calculate generalized Newtonian forces, their associated potentials and field equations, when other, in general non-extensive, entropies are considered instead of the usual…

This work reviews the understanding of the direction of time introduced by Hans Reichenbach, including the fundamental relation of the perceived flow of time to the second law of thermodynamics (i.e. the Boltzmann time hypothesis), and the…

A generalization of the Gibbs entropy postulate is proposed based on the BBGKY hierarchy as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that…

For several independent reasons, the idea that notorious sources of entropy could exist in the Universe has been recently revived. Taking advantage of a new framework accounting for non-equilibrium processes in cosmology, we explicitly…