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The role of entropy production and thermodynamic uncertainty relations in the asymmetric thermalization of open quantum systems

Álvaro Tejero

TL;DR

This work investigates why heating generally drives faster thermalization than cooling in open quantum systems by linking entropy production to dynamical barriers. Using a GKSL framework with a single bosonic bath, it derives how heating yields a larger spectral gap and stronger coupling to the dominant relaxation mode, producing a higher initial entropy production rate and faster convergence to the hot Gibbs state. The study furthermore employs the quantum thermokinetic uncertainty relation (TKUR) to connect heat-current fluctuations with thermodynamic cost, showing heating achieves greater dynamical activity and tighter current-precision bounds, thereby reducing fluctuations and accelerating equilibration. Through an analytically tractable thermal qubit model, the authors demonstrate these mechanisms explicitly and discuss implications for quantum thermal machines, highlighting a fundamental speed-versus-precision trade-off in nonequilibrium quantum dynamics.

Abstract

The asymmetry between heating and cooling in open quantum systems is a hallmark of nonequilibrium dynamics, yet its thermodynamic origin has remained unclear. Here, we investigate the thermalization of a quantum system weakly coupled to a thermal bath, focusing on the entropy production rate and the quantum thermokinetic uncertainty relation (TKUR). We derive an analytical expression for the entropy production rate, showing that heating begins with a higher entropy production, which drives faster thermalization than cooling. The quantum TKUR links this asymmetry to heat-current fluctuations, demonstrating that larger entropy production suppresses fluctuations, making heating more stable than cooling. Our results reveal the thermodynamic basis of asymmetric thermalization and highlight uncertainty relations as key to nonequilibrium quantum dynamics.

The role of entropy production and thermodynamic uncertainty relations in the asymmetric thermalization of open quantum systems

TL;DR

This work investigates why heating generally drives faster thermalization than cooling in open quantum systems by linking entropy production to dynamical barriers. Using a GKSL framework with a single bosonic bath, it derives how heating yields a larger spectral gap and stronger coupling to the dominant relaxation mode, producing a higher initial entropy production rate and faster convergence to the hot Gibbs state. The study furthermore employs the quantum thermokinetic uncertainty relation (TKUR) to connect heat-current fluctuations with thermodynamic cost, showing heating achieves greater dynamical activity and tighter current-precision bounds, thereby reducing fluctuations and accelerating equilibration. Through an analytically tractable thermal qubit model, the authors demonstrate these mechanisms explicitly and discuss implications for quantum thermal machines, highlighting a fundamental speed-versus-precision trade-off in nonequilibrium quantum dynamics.

Abstract

The asymmetry between heating and cooling in open quantum systems is a hallmark of nonequilibrium dynamics, yet its thermodynamic origin has remained unclear. Here, we investigate the thermalization of a quantum system weakly coupled to a thermal bath, focusing on the entropy production rate and the quantum thermokinetic uncertainty relation (TKUR). We derive an analytical expression for the entropy production rate, showing that heating begins with a higher entropy production, which drives faster thermalization than cooling. The quantum TKUR links this asymmetry to heat-current fluctuations, demonstrating that larger entropy production suppresses fluctuations, making heating more stable than cooling. Our results reveal the thermodynamic basis of asymmetric thermalization and highlight uncertainty relations as key to nonequilibrium quantum dynamics.

Paper Structure

This paper contains 14 sections, 51 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dynamics
  4. Entropy production rate and thermodynamic uncertainty relations
  5. Quantification of the thermalization speed
  6. Approximated expression for the entropy production rate
  7. Heating vs cooling
  8. Thermal qubit
  9. Dynamics and entropy production
  10. Uncertainty relations
  11. Implications for asymmetry
  12. Conclusion
  13. Acknowledgements
  14. Orthogonality of the weighted inner product for right eigenmatrices

Figures (1)

  • Figure 1: Inverse dynamical activity, and inverse entropy production rate, for the thermalization of the thermal qubit. The red area represents the heating process whereas the blue one is the cooling one. The initial temperature in the plot has been set to $\beta_0 = 5$ (vertical dashed line), where the arrows represent the direction of the inverse temperature: heating from the central line to the left, and cooling from the central line to the right. The parameters are $\hbar \omega =1, \gamma =0.1$.