Abstract
The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics. In this paper, by considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers. The results indicate that the first one can be interpreted as a measure of how fast the system is trying to approach the local equilibrium, while the second one as the local equilibrium lattice temperature. We also provide the explicit expression of the macroscopic entropy density for the system of phonons, by which we theoretically explain the approach of the system toward equilibrium and characterize the nature of the equilibria, in the spatially homogeneous case.
Highlights
The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics
By considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers
In [9,10] electro-thermal effects were analyzed by a Monte Carlo simulation, adapting the method in [13,14,15] with a description of the phonon–phonon scatterings based on a Bhatnagar–Gross–Krook (BGK) approximation, where a proper definition of a local temperature of the graphene crystal lattice is needed
Summary
The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics (for a comprehensive review, the interested reader is referred to [1,2,3,4]). In [9,10] electro-thermal effects were analyzed by a Monte Carlo simulation (for results based on a finite difference scheme, see [11]; for results based on a discontinuous Galerkin scheme, see [12]), adapting the method in [13,14,15] with a description of the phonon–phonon scatterings based on a Bhatnagar–Gross–Krook (BGK) approximation, where a proper definition of a local temperature of the graphene crystal lattice is needed This latter is deduced from the conservation properties of the phonon–phonon collision terms.
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