Extended Nonequilibrium Variables for 1D Hyperbolic Heat Conduction

  • 1 Institute of Problems of Chemical Physics, Academy of Sciences of Russia, Chernogolovka, Russia
  • 2 Samara State Technical University, ul. Molodogvardeiskaya 244, Samara, Russia
Sergey L. SobolevORCID iD: https://orcid.org/0000-0002-8156-710X
  • Corresponding author
  • 104752Institute of Problems of Chemical Physics, Academy of Sciences of Russia, Chernogolovka, Moscow Region, 142432, Russia
  • 65056Samara State Technical University, ul. Molodogvardeiskaya 244, Samara, 443100, Russia
  • orcid.org/0000-0002-8156-710X
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and Igor V. Kudinov

Abstract

We use the Shannon (information) entropy to define an “entropic” temperature for 1D nonequilibrium system with heat flux. In contrast to the kinetic temperature, which is related to the average kinetic energy, the nonequilibrium entropic temperature is related to the changes in entropy and serves as a criterion for thermalization. However, the direction and value of the heat flux is controlled by the gradient of the kinetic temperature, whereas space-time evolution and the space-time evolution of the heat flux are governed by the hyperbolic heat conduction equation. The extended nonequilibrium variables, namely, entropy, entropic temperature, thermal conductivity, and heat capacity demonstrate a third-law-like behavior at high deviation from equilibrium when the heat flux tends to its maximum value, even at nonzero value of the kinetic temperature. The ratio of the heat flux to its maximum possible value plays a role of an order parameter – it varies from zero in the equilibrium (disordered) state to unity in the nonequilibrium (ordered) state.

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The Journal of Non-Equilibrium Thermodynamics serves as an international publication organ for new ideas, insights and results on non-equilibrium phenomena in science, engineering and related natural systems. The central aim of the journal is to provide a bridge between science and engineering and to promote scientific exchange on non-equilibrium phenomena and on analytic or numeric modeling for their interpretation.

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