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Licensed Unlicensed Requires Authentication Published by De Gruyter March 14, 2020

Extended Nonequilibrium Variables for 1D Hyperbolic Heat Conduction

  • Sergey L. Sobolev ORCID logo EMAIL logo 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.

Award Identifier / Grant number: 20-38-70021

Funding statement: The reported study was funded by RFBR, project number 20-38-70021. This work was performed in accordance with the state task registration No. 0089-2019-0002.

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Received: 2020-01-21
Accepted: 2020-02-24
Published Online: 2020-03-14
Published in Print: 2020-07-26

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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