Classical random field viewpoint to Gorini-Kossakowski-Sudarshan-Lindblad equation and its linear and nonlinear generalizations

Abstract

We show that the basic equation of theory of open systems, Gorini-Kossakowski-Sudarshan-Lindblad equation, as well as its linear and nonlinear generalizations have a natural classical probabilistic interpretation - in the framework of prequantum classical statistical field theory. The latter gives an example of a classical probabilistic model (with random fields as subquantum variables) reproducing the basic probabilistic predictions of quantum mechanics.