Entropy Linear Response Theory with Non-Markovian Bath

TL;DR

This paper introduces a perturbative entropy response theory for non-Markovian environments, revealing universal spectral dependencies, different growth regimes, and novel entanglement behaviors including Page curve-like dynamics.

Contribution

It develops a general perturbative framework for entropy dynamics without Markovian assumptions, applicable to bosonic and fermionic environments, and uncovers new entropy behaviors and dualities.

Findings

Renyi entropy response depends on spectral functions and statistical kernels.

Short-time t^2 growth and long-time t linear growth in entropy observed.

Page curve-like entanglement dynamics found in a black hole analogy.

Abstract

We developed a perturbative calculation for entropy dynamics considering a sudden coupling between a system and a bath. The theory we developed can work in general environment without Markovian approximation. A perturbative formula is given for bosonic environment and fermionic environment, respectively. We find the Renyi entropy response is only related to the spectral functions of the system and the environment, together with a specific statistical kernel distribution function. We find a t^2 growth/decay in the short time limit and a t linear growth/decay in longer time scale for second Renyi entropy. A non-monotonic behavior of Renyi entropy for fermionic systems is found to be quite general when the environment's temperature is lower. A Fourier's law in heat transport is obtained when two systems' temperature are close to each other. A consistency check is made for Sachdev-Ye-Kitaev model coupling to free fermions, a Page curve alike dynamics is found in a process dual to black hole evaporation. An oscillation of entanglement entropy is found for a gapped spectrum of environment.