Positive Processes

Abstract

In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive algebras, the spectral potential, the dual entropy, equilibrium measures, the action functional, sensitive states, empirical measures and prove within it the law of large numbers with respect to the sensitive states and calculate asymptotics for probabilities of large deviations in terms of the action functional.