Artículo
Global stability and H theorem in lattice models with nonconservative interactions
Autor/es | Plata Ramos, Carlos Alberto
Prados Montaño, Antonio |
Departamento | Universidad de Sevilla. Departamento de Física Atómica, Molecular y Nuclear |
Fecha de publicación | 2017 |
Fecha de depósito | 2020-04-28 |
Publicado en |
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Resumen | In kinetic theory, a system is usually described by its one-particle distribution function f (r,v,t), such that
f (r,v,t)drdv is the fraction of particles with positions and velocities in the intervals (r,r + dr) and (v,v ... In kinetic theory, a system is usually described by its one-particle distribution function f (r,v,t), such that f (r,v,t)drdv is the fraction of particles with positions and velocities in the intervals (r,r + dr) and (v,v + dv), respectively. Therein, global stability and the possible existence of an associated Lyapunov function or H theorem are open problems when nonconservative interactions are present, as in granular fluids. Here, we address this issue in the framework of a lattice model for granularlike velocity fields. For a quite general driving mechanism, including both boundary and bulk driving, we show that the steady state reached by the system in the long-time limit is globally stable. This is done by proving analytically that a certain H functional is nonincreasing in the long-time limit. Moreover, for a quite general energy injection mechanism, we are able to demonstrate that the proposed H functional is nonincreasing for all times. Also, we put forward a proof that clearly illustrates why the “classical” Boltzmann functional HB[f ] = dr dvf (r,v,t) ln f (r,v,t) is inadequate for systems with nonconservative interactions. This is done not only for the simplified kinetic description that holds in the lattice models analyzed here but also for a general kinetic equation, like Boltzmann’s or Enskog’s. |
Cita | Plata Ramos, C.A. y Prados Montaño, A. (2017). Global stability and H theorem in lattice models with nonconservative interactions. Physical Review E, 95 (5, 052121), 1-12. |
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