Master equations with canonical invariance

Abstract

It is shown that there exists a large variety of master equations with the property that the canonical equilibrium distribution becomes a solution on replacing the temperature with a suitable function of time. The additional requirement of detailed balance, however, strongly restricts the possibilities and uniquely leads to only three special forms of the master equation, given by equations (17), (22), and (23). These equations are the same as found by Andersen, Oppenheim, Shuler, and Weiss. Other requirements than detailed balance are also briefly discussed.