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Open AccessArticle

Kullback–Leibler Divergence of a Freely Cooling Granular Gas

1
Departamento de Física, Universidad de Extremadura, E-06006 Badajoz, Spain
2
Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(11), 1308; https://doi.org/10.3390/e22111308
Received: 7 October 2020 / Revised: 6 November 2020 / Accepted: 13 November 2020 / Published: 17 November 2020
(This article belongs to the Special Issue Entropy: The Scientific Tool of the 21st Century)
Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original H-theorem hypotheses do not fit here and the H-functional presents some additional measure problems that are solved by the Kullback–Leibler divergence (KLD) of a reference velocity distribution function from the actual distribution. The right choice of the reference distribution in the KLD is crucial for the latter to qualify or not as a Lyapunov functional, the asymptotic “homogeneous cooling state” (HCS) distribution being a potential candidate. Due to the lack of a formal proof far from the quasielastic limit, the aim of this work is to support this conjecture aided by molecular dynamics simulations of inelastic hard disks and spheres in a wide range of values for the coefficient of restitution (α) and for different initial conditions. Our results reject the Maxwellian distribution as a possible reference, whereas they reinforce the HCS one. Moreover, the KLD is used to measure the amount of information lost on using the former rather than the latter, revealing a non-monotonic dependence with α. View Full-Text
Keywords: Kullback–Leibler divergence; granular gases; kinetic theory; molecular dynamics Kullback–Leibler divergence; granular gases; kinetic theory; molecular dynamics
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MDPI and ACS Style

Megías, A.; Santos, A. Kullback–Leibler Divergence of a Freely Cooling Granular Gas. Entropy 2020, 22, 1308. https://doi.org/10.3390/e22111308

AMA Style

Megías A, Santos A. Kullback–Leibler Divergence of a Freely Cooling Granular Gas. Entropy. 2020; 22(11):1308. https://doi.org/10.3390/e22111308

Chicago/Turabian Style

Megías, Alberto; Santos, Andrés. 2020. "Kullback–Leibler Divergence of a Freely Cooling Granular Gas" Entropy 22, no. 11: 1308. https://doi.org/10.3390/e22111308

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