Classical Markovian Kinetic Equations: Explicit Form and H-Theorem
| dc.creator | Tzanakis, Constantinos | |
| dc.creator | Grecos, Alkis P. | |
| dc.date | 1997-08-27 | |
| dc.date.accessioned | 2026-07-07T10:15:51Z | |
| dc.date.available | 2026-07-07T10:15:51Z | |
| dc.description | The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such a kinetic equation in the Heisenberg representation, define Markov semigroups on the space of observables. Moreover, a general H-theorem for the adjoint of such semigroups is formulated and proved provided that at least locally, an invariant measure exists. Under a certain continuity assumption, the Markov semigroup property is sufficient for a linear kinetic equation to be a second order differential equation with nonegative-definite leading coefficient. Conversely it is shown that such equations define Markov semigroups satisfying an H-theorem, provided there exists a nonnegative equilibrium solution for their formal adjoint, vanishing at infinity. | |
| dc.description | 25pp, LATEX | |
| dc.identifier | https://arxiv.org/abs/physics/9708031 | |
| dc.identifier | http://arxiv.org/abs/physics/9708031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173312 | |
| dc.subject | Mathematical Physics | |
| dc.title | Classical Markovian Kinetic Equations: Explicit Form and H-Theorem | |
| dc.type | text |