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Superstatistics, thermodynamics, and fluctuations.

Sumiyoshi Abe1, Christian Beck, Ezechiel G D Cohen

  • 1Department of Physical Engineering, Mie University, Tsu, Mie 514-8507, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
PubMed
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A new thermodynamiclike formalism using conditional entropies is introduced for superstatistical systems. This framework accounts for variations in intensive variables in nonequilibrium states, extending ordinary thermodynamics.

Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Non-equilibrium Systems

Background:

  • Superstatistical systems exhibit complex behaviors not fully captured by traditional thermodynamics.
  • Understanding large-scale variations of intensive variables in nonequilibrium stationary states is crucial.

Purpose of the Study:

  • To develop a thermodynamiclike formalism for superstatistical systems.
  • To incorporate conditional entropies to account for system variations.
  • To generalize existing thermodynamic relations for broader applicability.

Main Methods:

  • Development of a formalism based on conditional entropies.
  • Analysis of systems in nonequilibrium stationary states.
  • Application of maximum entropy principles.

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Main Results:

  • A thermodynamiclike formalism for superstatistical systems is established.
  • The theory recovers ordinary thermodynamics as a special case.
  • Corrections to ordinary thermodynamics can be systematically evaluated.
  • A generalization of Einstein's relation for fluctuations is presented.

Conclusions:

  • The developed formalism provides a robust framework for studying superstatistical systems.
  • This approach offers a more comprehensive understanding of systems in nonequilibrium stationary states.
  • The generalized Einstein relation enhances the analysis of fluctuations in these systems.