Related papers: What is Entropy?
The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…
In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
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…
Diffusivity, a measure for how rapidly a fluid self-mixes, shows an intimate, but seemingly fragmented, connection to thermodynamics. On one hand, the "configurational" contribution to entropy (related to the number of mechanically-stable…
We derive a formula for the nonequilibrium entropy of a classical stochastic field in terms of correlation functions of this field. The formalism is then applied to define the entropy of gravitational perturbations (both gravitational waves…
We prove a proposition that the entropy of the system composed of finite $N$ molecules of ideal gas is the $q$-entropy or Havrda-Charv\'at-Tsallis entropy, which is also known as Tsallis entropy, with the entropic index…
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems…
This pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature; being derived from the usual, often termed Boltzmann, definition of entropy. First, both the Boltzmann and Gibbs…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
A quantitative analysis of the process of condensation of bosons both in harmonic traps and in gases is made resorting to two ingredients only: Bose classical distribution and spectral discretness. It is shown that in order to take properly…
Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs'…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
Informational entropy is often identified as physical entropy. This is surprising because the two quantities are differently defined and furthermore the former is a subjective quantity while the latter is an objective one. We describe the…
Entropy and temperature of a system in a coherent state are naturally defined on a base of a density matrix of the system. As an example, entropy and temperature are evaluated for coherent states of a harmonic oscillator and quantum field…
We compute the entanglement entropy of soft gluons in the wave function of a fast moving hadron and discuss its basic properties. We also derive the expression for entropy production in a high energy hadronic collision within the Color…