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Determining the Tsallis parameter via maximum entropy.

J M Conroy1, H G Miller1

  • 1Department of Physics, The State University of New York at Fredonia, Fredonia, New York 14063.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2015
PubMed
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This study presents two methods for determining the Tsallis parameter q, which is crucial for nonextensive entropy. The approach depends on system constraints, allowing q to be a variable or a fixed value derived from data.

Area of Science:

  • Statistical Mechanics
  • Nonextensive Thermodynamics

Background:

  • The Tsallis entropic measure introduces a parameter q that requires determination.
  • Phenomenological applications sometimes necessitate q to be a variable, not a constant.

Purpose of the Study:

  • To present two distinct methods for determining the Tsallis parameter q.
  • To explore scenarios where q can be a function of a Lagrange multiplier or a fixed value.

Main Methods:

  • Solving an equivalent maximum entropy (maxent) problem for constraints of the form Tr(F(q)Ô)=C.
  • Utilizing an additional constraint equation to determine a fixed value of q when it cannot be expressed in the standard form.

Main Results:

  • Demonstrated that q can be determined as a function of the Lagrange multiplier in the first case.

Related Experiment Videos

  • Obtained the exact solution of the static generalized Fokker-Planck equation (GFPE) using maxent with Tsallis entropy.
  • Showcased that an additional constraint can be used to determine a fixed q value.

    • Conclusions:

    • The determination of q is system-dependent and can be approached via maxent or additional constraints.
    • The study provides a framework for handling variable or fixed Tsallis parameter q in different physical systems.