Canonical equilibrium distribution derived from Helmholtz potential

Thomas Oikonomou, G. Baris Bagci, Ugur Tirnakli

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.

Original languageEnglish
Pages (from-to)6386-6389
Number of pages4
JournalPhysica A: Statistical Mechanics and its Applications
Volume391
Issue number24
DOIs
Publication statusPublished - Dec 15 2012
Externally publishedYes

Fingerprint

Equilibrium Distribution
Hermann Von Helmholtz
Tsallis Entropy
Probability Distribution
entropy
Entropy Maximization
Canonical Ensemble
derivation
Alternatives
Electromagnetic Fields
Free Energy
Power Law
uniqueness
Uniqueness
Trace
Entropy
free energy

Keywords

  • Canonical equilibrium distribution
  • Helmholtz free energy
  • Tsallis entropy

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistics and Probability

Cite this

Canonical equilibrium distribution derived from Helmholtz potential. / Oikonomou, Thomas; Baris Bagci, G.; Tirnakli, Ugur.

In: Physica A: Statistical Mechanics and its Applications, Vol. 391, No. 24, 15.12.2012, p. 6386-6389.

Research output: Contribution to journalArticle

@article{1d3c885b8f6f403fb3d89d3b1078fa60,
title = "Canonical equilibrium distribution derived from Helmholtz potential",
abstract = "Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.",
keywords = "Canonical equilibrium distribution, Helmholtz free energy, Tsallis entropy",
author = "Thomas Oikonomou and {Baris Bagci}, G. and Ugur Tirnakli",
year = "2012",
month = "12",
day = "15",
doi = "10.1016/j.physa.2012.07.072",
language = "English",
volume = "391",
pages = "6386--6389",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "24",

}

TY - JOUR

T1 - Canonical equilibrium distribution derived from Helmholtz potential

AU - Oikonomou, Thomas

AU - Baris Bagci, G.

AU - Tirnakli, Ugur

PY - 2012/12/15

Y1 - 2012/12/15

N2 - Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.

AB - Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.

KW - Canonical equilibrium distribution

KW - Helmholtz free energy

KW - Tsallis entropy

UR - http://www.scopus.com/inward/record.url?scp=84865863983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865863983&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2012.07.072

DO - 10.1016/j.physa.2012.07.072

M3 - Article

AN - SCOPUS:84865863983

VL - 391

SP - 6386

EP - 6389

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 24

ER -