Linear and nonlinear stochastic processes

by R. F. Streater.

This constitutes pp 343-353 in "Quantum Probability and Applications III", eds. L. Accardi and W. von Waldenfels, Springer Lecture Notes 1303, 1986. ISBN 3-540-18919-X.

ABSTRACT

We discuss the two main areas in non-equilibrium statistical physics. In the first, a finite system is coupled to an infinite heat bath at a given temperature. The coupling obeys detailed balance and the system approaches the temperature of the heat bath at large times. In the second type of problem, the system is isolated, and the dynamics leads to an equilibrium state at a temperature determined by the initial energy. We argue that such a system must obey equations of motion that are nonlinear in the state. We illustrate the idea with simple examples of the Boltzmann equation.

REMARK

The models obey both the first law and the second law of thermodynamics: mean energy, including heat energy, is conserved, and the entropy increases in time. This work was the origin of the later theory, statistical dynamics.