Properties of Statistical Equilibrium Equations: Positivity and Uniqueness

摘要

While linear statistical equilibrium equations play an important role in the description of nonequilibrium processes in astrophysics, some of their basic mathematical properties, such as uniqueness and positivity, have not been fully explored. In this paper these properties are related to concepts of connectivity from the theory of continuous-time Markov chains. For the irreducible case (in which every state is connected to every other state, either directly or through intermediate states), the solution is shown to be positive and unique when one positive normalization condition is provided.