Interrelations between Stochastic Equations for Systems with Pair Interactions
Abstract
Several types of stochastic equations are important in thermodynamics, chemistry, evolutionary biology, population dynamics and quantitative social science. For systems with pair interactions four different types of equations are derived, starting from a master equation for the state space: First, general mean value and (co)variance equations. Second, Boltzmannlike equations. Third, a master equation for the configuration space allowing transition rates which depend on the occupation numbers of the states. Fourth, a FokkerPlanck equation and a ``BoltzmannFokkerPlanck equation''. The interrelations of these equations and the conditions for their validity are worked out clearly. A procedure for a selfconsistent solution of the nonlinear equations is proposed. Generalizations to interactions between an arbitrary number of systems are discussed.
 Publication:

arXiv eprints
 Pub Date:
 May 1998
 DOI:
 10.48550/arXiv.condmat/9805256
 arXiv:
 arXiv:condmat/9805256
 Bibcode:
 1998cond.mat..5256H
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 For related work see http://www.theo2.physik.unistuttgart.de/helbing.html