Related papers: Renyi statistics in equilibrium statistical mechan…
The division by N! in the expression of statistical entropy is usually justified to students by the statement that classical particles should be counted as indistinguishable. Sometimes, quantum indistinguishability is invoked to explain it.…
Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is…
We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non-relativistic ideal Fermi-gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio and others…
This paper seeks to establish a connection between the cosmological constant and Renyi entropy within the framework of Kalb-Raymond(K-R) gravity. Our analysis is supported by evidence showing the equivalence of the thermodynamic topology of…
In low-dimensional systems, indistinguishable particles can display statistics that interpolate between bosons and fermions. Signatures of these "anyons" have been detected in two-dimensional quasiparticle excitations of the fractional…
In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the R\'{e}nyi divergences between the initial…
This is full length article (draft version) where problem number of topics in Topic Modeling is discussed. We proposed idea that Renyi and Tsallis entropy can be used for identification of optimal number in large textual collections. We…
A simplified thermodynamic approach of the incompressible axisymmetric Euler equations is considered based on the conservation of helicity, angular momentum and microscopic energy. Statistical equilibrium states are obtained by maximizing…
This study shows that the generalized Boltzmann distribution is the only distribution mathematically consistent with thermodynamics when the system is described by an ensemble of a certain mathematical form. This mathematical form is very…
We study in great detail the possible existence of a Renyi-associated thermodynamics, with negative results. In particular, we uncover a hidden relation in the Renyi's variational problem (MaxEnt). This relation connects the two associated…
We show that the recently discovered thermodynamic equivalence between noninteracting Bose and Fermi gases in two dimensions, and between one-dimensional Bose and Fermi systems with linear dispersion, both in the grand-canonical ensemble,…
A picture for thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations…
The lack of a procedure to determine equilibrium thermodynamic properties of a small system interacting with a bath is frequently seen as a weakness of conventional statistical mechanics. A typical example for such a small system is a…
We show that typical Renyi's statistical mechanics' quantifiers exhibit poles. We are referring to the partition function ${\cal Z}$ and the mean energy $<{\cal U}>$. Renyi's entropy is characterized by a real parameter $\alpha$. The poles…
Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed…
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…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
In a recent article, Werndl and Frigg discuss the relationship between the Boltzmannian and Gibbsian framework of statistical mechanics, addressing in particular the question when equilibrium values calculated in both frameworks agree. In…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…