Hierarchical Equations of Motion Approach to Quantum Thermodynamics

TL;DR

This paper introduces a hierarchical equations of motion framework for analyzing quantum thermodynamics, enabling accurate modeling of non-Markovian interactions, strong coupling, and correlations, crucial for understanding heat transfer and thermodynamic laws.

Contribution

It develops a numerically exact formalism to incorporate system-bath correlations and entanglement in quantum thermodynamics, surpassing traditional quantum master equations.

Findings

TPC significantly affects heat transfer in quantum systems.

The formalism accurately captures thermodynamic laws in complex models.

System-bath entanglement influences heat current beyond energy flow.

Abstract

We present a theoretical framework to investigate quantum thermodynamic processes under non-Markovian system-bath interactions on the basis of the hierarchical equations of motion (HEOM) approach, which is convenient to carry out numerically "exact" calculations. This formalism is valuable because it can be used to treat not only strong system-bath coupling but also system-bath correlation or entanglement, which will be essential to characterize the heat transport between the system and quantum heat baths. Using this formalism, we demonstrated an importance of the thermodynamic effect from the tri-partite correlations (TPC) for a two-level heat transfer model and a three-level autonomous heat engine model under the conditions that the conventional quantum master equation approaches are failed. Our numerical calculations show that TPC contributions, which distinguish the heat current from the energy current, have to be take into account to satisfy the thermodynamic laws.