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Entropy
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Review Papers for Entropy, Second Edition
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Review Papers for Entropy, Second Edition

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Entropy Reviews".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1419

Editor

Prof. Dr. J. Miguel Rubi

E-Mail Website
Guest Editor
Department of Condensed Matter Physics, University of Barcelona, 08007 Barcelona, Spain
Interests: non-equilibrium thermodynamics; non-equilibrium statistical physics; thermodynamics of small systems; heat exchange at the nanoscale; Casimir forces; diffusion in confined systems; small biological systems; non-equilibrium self-assembly
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Special Issue Information

Dear Colleagues,

The main objective of this section is to publish review articles on topics of great current interest in which the concept of entropy plays a central role, and thus create a space where readers can find their most innovative ideas and applications. The concept of entropy developed in thermodynamics, statistics mechanics, and information theory has made a great impact on disciplines such as physics and physico-chemistry, engineering, biology, complex systems, and computer sciences in recent years. We are interested in receiving manuscripts that review theoretical, experimental, and computational studies on the topics included in such research areas.

Prof. Dr. J. Miguel Rubi
Guest Editor

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Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

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Review

52 pages, 1369 KB  
Review
Dynamic Properties in a Collisional Model for Confined Granular Fluids: A Review
by Ricardo Brito, Rodrigo Soto and Vicente Garzó
Entropy 2026, 28(4), 454; https://doi.org/10.3390/e28040454 - 15 Apr 2026
Viewed by 564
Abstract
Granular systems confined in a shallow box and subjected to vertical vibration provide an attractive geometry for studying fluidized granular media. In this configuration, grains acquire kinetic energy in the vertical direction through collisions with the confining walls, and this energy is subsequently [...] Read more.
Granular systems confined in a shallow box and subjected to vertical vibration provide an attractive geometry for studying fluidized granular media. In this configuration, grains acquire kinetic energy in the vertical direction through collisions with the confining walls, and this energy is subsequently transferred to the horizontal degrees of freedom via interparticle collisions. In recent years, the so-called Δ-model has been introduced as a simplified yet effective description of the dynamics of granular systems in such geometries. This review presents the results obtained from kinetic theory for the granular Δ-model. To model the energy transfer mechanism, a fixed velocity increment Δ is added to the normal component of the relative velocity during collisions. In this way, the vertical motion is effectively integrated out while retaining the collisional energy injection characteristic of the confined setup. This mechanism compensates for the energy loss due to inelastic collisions and leads to stable homogeneous steady states that can be analyzed within the framework of kinetic theory. The Enskog kinetic equation is formulated for this model and first analyzed in homogeneous steady states, yielding the stationary temperature and the equation of state. The dynamics of inhomogeneous states is then investigated using the Chapman–Enskog method, from which the Navier–Stokes transport coefficients are derived. The theory is further extended to granular mixtures, in which particles may differ in mass, size, restitution coefficient, or in the value of Δ. In this case, the phenomenology becomes richer; for example, energy equipartition is violated even in homogeneous steady states. The mixture dynamics is studied through the corresponding Navier–Stokes equations, and the associated transport coefficients are obtained in the low-density regime. The analysis of the hydrodynamic equations shows that, in agreement with simulations, the homogeneous state is linearly stable. Moreover, the intrinsically nonequilibrium nature of the model leads to the violation of Onsager reciprocity relations in granular mixtures. The theoretical predictions exhibit in general good agreement with both molecular dynamics simulations and direct simulation Monte Carlo results. Full article
(This article belongs to the Special Issue Review Papers for Entropy, Second Edition)
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