Inverse Liouville problem

Journal Article · Sun Jun 01 04:00:00 EDT 1980 · Hadronic J.; (United States)

OSTI ID:6444606

Grmela, M ^[1]; Fronteau, J; Tellez-Arenas, A

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1. Univ. of Montreal, Quebec

Liouville's theorem, in its original form (1838), allows us to derive a kinetic equation from any given dynamics, whether conservative or not. In this article we study the inverse problem: given a kinetic equation, to find quasi-particle dynamics (generally non-conservative) which, via Liouville's theorem, generates precisely this equation. The mathematical problem thus presented allows an infinite number of solutions. In fact, physically, we are allowed, by what we call the principle of correspondence, to retain one particular non-conservative set of dynamics, namely that which becomes conservative when statistical equilibrium is reached. From this viewpoint, we give the solution to the inverse Liouville problem for a very general class of kinetic equations. This solution has a direct physical interpretation in terms of current velocity. We consider in particular the cases of the Boltzmann and Fokker-Planck equations.

• OSTI ID: 6444606
• Journal Information: Hadronic J.; (United States), Journal Name: Hadronic J.; (United States) Vol. 3:4; ISSN HAJOD
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics & Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOLTZMANN EQUATION
DIFFERENTIAL EQUATIONS
DYNAMICS
EQUATIONS
FOKKER-PLANCK EQUATION
KINETIC EQUATIONS
LIOUVILLE THEOREM
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES