Classical Markovian Kinetic Equations: Explicit Form and H-Theorem

Details Classical Markovian Kinetic Equations: Explicit Form and H-Theorem Classical Markovian Kinetic Equations: Explicit Form and H-Theorem

1997-08-27

arxiv.org/abs/physics/9708031v1

Physics

Mathematical Physics

25pp, LATEX

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Classical Markovian Kinetic Equations: Explicit Form and H-Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classical Markovian Kinetic Equations: Explicit Form and H-Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical Markovian Kinetic Equations: Explicit Form and H-Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-177581