Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

Abstract

This work presents the thermodynamical analysis of the ballistic heat equation from the viewpoint of two approaches: Classical Irreversible Thermodynamics (CIT) and Extended Irreversible Thermodynamics (EIT). A formula for calculation of the entropy within the framework of EIT for the ballistic heat equation is derived in this work. Entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and the entropy production can be negative. The results obtained with EIT show that the entropy is a monotonic function and the entropy production is nonnegative. An approximative formula for the asymptotic behavior of the entropy for the ballistic heat equation is obtained. A comparison with the ordinary Fourier-based heat equation and hyperbolic heat equation is made. A crucial difference in asymptotic behaviour of the entropy for ballistic and classical heat conduction equation is shown. It is shown that mathematical time reversibility of partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase.

arXiv comment9 pages, 1 figure, 2 table, comments on discreet consideration of the problem are added, minor language corrections are added

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Cited by in corpus (3)

• Ballistic resonance and thermalization in Fermi-Pasta-Ulam-Tsingou chain at finite temperature
• Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source
• Thermal equilibration in a one-dimensional damped harmonic crystal