Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion

Simone Artini, Gabriele Lo Monaco, Alberto Imparato, Mauro Paternostro, Sandro Donadi

Abstract

We rigorously analyze the non-equilibrium thermodynamic behavior of various formulations of quantum Brownian motion (QBM) using the framework of stochastic thermodynamics. While the widely used Caldeira-Leggett master equation exhibits desirable thermodynamic features, such as the fulfilment of a detailed balance, it fails to ensure complete positivity. In contrast, several completely positive and trace-preserving (CPTP) extensions turn out to be thermodynamically controversial. We show that such extensions introduce anomalous phase-space structures that violate detailed balance at the steady state, leading to non-vanishing entropy production and effective non-equilibrium current of unclear physical origins. Our results highlight a fundamental tension between quantum consistency and thermodynamic equilibration in open quantum systems.

Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion

Abstract

We rigorously analyze the non-equilibrium thermodynamic behavior of various formulations of quantum Brownian motion (QBM) using the framework of stochastic thermodynamics. While the widely used Caldeira-Leggett master equation exhibits desirable thermodynamic features, such as the fulfilment of a detailed balance, it fails to ensure complete positivity. In contrast, several completely positive and trace-preserving (CPTP) extensions turn out to be thermodynamically controversial. We show that such extensions introduce anomalous phase-space structures that violate detailed balance at the steady state, leading to non-vanishing entropy production and effective non-equilibrium current of unclear physical origins. Our results highlight a fundamental tension between quantum consistency and thermodynamic equilibration in open quantum systems.

Paper Structure

This paper contains 4 sections, 2 theorems, 39 equations, 1 table.

Table of Contents

  1. Detailed Balance and stochastic thermodynamics
  2. Going from the master equation to the Fokker-Planck equation
  3. On different choices of entropy production
  4. Relation with the KMS Detailed Balance

Key Result

Theorem 1

For a homogeneous Fokker-Planck equation such that ${\mathcal{E}}{\bm B}{\mathcal{E}}^T={\bm B}$, if a stationary solution $P_S(\bm x)$ exists and is such that the irreversible component of the current is zero, then the DB conditions hold. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (3)

  • Theorem
  • Theorem
  • proof