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Equilibrium States in Two-Temperature Systems.

Evaldo M F Curado1, Fernando D Nobre1

  • 1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Urca, Rio de Janeiro 22290-180, Brazil.

Entropy (Basel, Switzerland)
|December 3, 2020
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Summary
This summary is machine-generated.

This study explores systems with two distinct temperatures, extending previous work on type-II superconductors. A new thermodynamic framework is proposed for systems with two conjugated temperatures and entropic forms.

Keywords:
generalized entropiesnonextensive thermostatisticsnonlinear Fokker-Planck equations

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Nonlinear Dynamics

Background:

  • Systems with multiple temperatures are typically found in nonequilibrium statistical mechanics.
  • Previous research identified a two-temperature equilibrium state in repulsive vortex systems, modeling type-II superconductors, with temperatures related to particle velocities (T) and positions (θ).

Purpose of the Study:

  • To investigate a more general scenario involving two distinct temperatures (θ1 and θ2) of potentially similar magnitudes.
  • To develop a thermodynamic framework for systems characterized by two temperatures and associated entropic forms.

Main Methods:

  • Analysis of a nonlinear Fokker-Planck equation where θ1 and θ2 act as diffusion coefficients.
  • Proof of an H-theorem linking the Fokker-Planck equation to a sum of two entropic forms.
  • Introduction of a functional Λ[P] and a thermodynamically conjugated temperature parameter γ(θ1, θ2).

Main Results:

  • Demonstration that the stationary state of the Fokker-Planck equation can be considered an equilibrium state characterized by two temperatures.
  • Identification of the condition that temperature parameters must be thermodynamically conjugated to distinct entropic forms.
  • Proposal of an alternative physical description using pairs of conjugated variables (temperature and entropy).

Conclusions:

  • The study establishes a consistent thermodynamic framework for systems with two distinct temperatures.
  • The equilibrium state distribution derived from the Fokker-Planck equation aligns with entropy extremization.
  • The findings offer a more general approach to understanding complex systems beyond single-temperature thermodynamics.