# Quantum features of macroscopic fields. Entropy and dynamics

## TL;DR

This paper develops a comprehensive macroscopic formalism for wave fields that incorporates quantum features, including entropy and dynamics, applicable to phenomena like superradiance and polarization optics.

## Contribution

It introduces a reduced state of field (RSF) formalism combining average fields and correlations, derived from quantum dynamical semigroups, unifying classical and quantum descriptions.

## Key findings

- Formalism includes random sources, dissipation, and scattering.
- Defines RSF entropy from quantum von Neumann entropy.
- Applicable to superradiance and polarization optics.

## Abstract

Macroscopic fields like electromagnetic, MHD, acoustic or gravitational waves are usually described by classical wave equations with possible additional damping terms and coherent sources. The aim of this paper is to develop a complete macroscopic formalism including random/thermal sources, dissipation and random scattering of waves by environment. The proposed reduced state of field (RSF) combines averaged field with the two-point correlation function called single-particle density matrix. The evolution equations for RSF is obtained by reduction of the generalized quasi-free dynamical semigroups describing irreversible evolution of bosonic quantum field and the definition of RSF's entropy follows from the von Neumann entropy of quantum field states. The presented formalism can be applied, for example, to superradiance phenomena and allows to unify the Mueller and Jones calculi in polarization optics.