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

TL;DR

This paper demonstrates that the Gorini-Kossakowski-Sudarshan-Lindblad equation and its generalizations can be interpreted classically through prequantum classical statistical field theory, linking quantum and classical probabilistic models.

Contribution

It introduces a classical probabilistic interpretation of quantum open system dynamics using prequantum classical statistical field theory, including nonlinear generalizations.

Findings

Classical probabilistic models can reproduce quantum predictions.

The GKS-Lindblad equation has a natural classical interpretation.

Nonlinear generalizations extend the classical analogy.

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.