Entropy flow in a parametric amplifier

TL;DR

This paper introduces a method to define and analyze entropy flow in systems with continuous spectra, like radiation, using a discretization approach, and applies it to a parametric amplifier to reveal insights into information release mechanisms.

Contribution

It proposes a novel entropy flow definition for continuous spectra systems and demonstrates its application to a parametric amplifier, linking entropy flow quenching to quantum coherences.

Findings

Output entropy flux vanishes at large times

Energy and photon number fluxes remain nonzero

Off-diagonal coherences relate to information release

Abstract

Computations of entropy in thermodynamics rely on discreteness of the spectra of the subsystems. We argue that, for cases with continuous spectra (typically, radiation), there is a useful definition of entropy flow based on discretizing the signal into Gabor's "atoms," say, by means of a windowed Fourier transform. In particular, applying this method to a parametric amplifier (paramp) driven by a classical pump and coupled to a zero-temperature Markovian bath, we find that the output entropy flux vanishes at large times, even though the energy and photon number fluxes remain nonzero. This is consistent with the manner in which the paramp is expected to release information about its initial state. We relate the quenching of the entropy flow to development of the off-diagonal coherences in the output and discuss possible relevance of this mechanism to the black-hole information problem. We also propose to use measurements of the off-diagonal coherences as a means of extracting the rates at which high-entropy subsystems release information to linear environments.