Related papers: Entropy formula of N-body system
This paper studies the use of the Tsallis Entropy versus the classic Boltzmann-Gibbs-Shannon entropy for classifying image patterns. Given a database of 40 pattern classes, the goal is to determine the class of a given image sample. Our…
Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This…
The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional…
We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the…
In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and…
Boltzmann defined the entropy of a macroscopic system in a macrostate $M$ as the $\log$ of the volume of phase space (number of microstates) corresponding to $M$. This agrees with the thermodynamic entropy of Clausius when $M$ specifies the…
We show that a natural realization of the thermostatistics of q-bosons can be built on the formalism of q-calculus and that the entire structure of thermodynamics is preserved if we use an appropriate Jackson derivative in place of the…
We study the entropy of small subsystems in thermalizing quantum many-body systems governed by local Hamiltonians. Assuming the eigenstate thermalization hypothesis, we derive an analytical formula for the von Neumann entropy of…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies,…
We consider a self-gravitating system consisting of perfect fluid with spherical symmetry. Using the general expression of entropy density, we extremize the total entropy $S$ under the constraint that the total number of particles is fixed.…
Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
The paper examines and critiques the expression of entropy as the logarithm of the number of quantum states of a physical system. Boltzmann method of expressing entropy as the logarithm of the number of states of a gas with a given total…
The maximum entropy principle in Tsallis statistics is reformulated in the mathematical framework of the q-product, which results in the unique non self-referential q-canonical distribution. As one of the applications of the present…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
We consider a boson gas on the stretched horizon of the Schwartzschild and Kerr black holes. It is shown that the gas is in a Bose-Einstein condensed state with the Hawking temperature $T_c=T_H$ if the particle number of the system be equal…
Entanglement is the fundamental quantum property behind the now popular field of quantum transport of information. This quantum property is incompatible with the separation of a single system into two uncorrelated subsystems. Consequently,…