[Paper Review] Thermodynamically consistent dynamics of driven open quantum systems: from an autonomous framework to the semi-classical description

Roie Dann, Ronnie Kosloff|arXiv (Cornell University)|Dec 14, 2020

Spectroscopy and Quantum Chemical Studies4 citations

TL;DR

This paper develops a thermodynamically consistent master equation for driven open quantum systems by treating the drive as a large transient control system within an autonomous framework. By partitioning control and primary systems, it derives a semi-classical description where the drive appears as a time-dependent term in the Hamiltonian, with dynamics governed by eigenoperators of the driven free evolution; the theory is validated using a qubit coupled to a bosonic mode in a coherent state.

ABSTRACT

The structure of a thermodynamically consistent master equation for a driven system is obtained by imposing a set of thermodynamic postulates. The analysis is based on a time-independent autonomous construction, incorporating the drive as a large transient control quantum system. Under these assumptions, by partitioning the control and primary system we derive the semi-classical description. In this framework, the drive is incorporated as a time-dependent term in the primary system Hamiltonian. The resulting structure of the master equation is determined by a set of eigenoperators of the driven free dynamics. We demonstrate the theory by analyzing a qubit controlled by a single bosonic mode in a coherent state.

Motivation & Objective

• To establish a thermodynamically consistent framework for driven open quantum systems.
• To resolve inconsistencies in existing master equations by embedding the drive within an autonomous quantum control system.
• To derive a semi-classical description where the drive enters as a time-dependent term in the primary system Hamiltonian.
• To ensure the resulting master equation respects fundamental thermodynamic postulates such as detailed balance and entropy production.

Proposed method

• Formulate a time-independent autonomous quantum system that includes both the primary system and a large control system representing the drive.
• Partition the total Hilbert space into control and primary system subspaces to derive the reduced dynamics.
• Apply thermodynamic postulates (e.g., detailed balance, positivity of entropy production) to constrain the form of the master equation.
• Identify the eigenoperators of the driven free dynamics as the fundamental building blocks of the master equation.
• Derive the semi-classical limit by taking the control system to be in a coherent state, leading to a time-dependent Hamiltonian for the primary system.
• Validate the framework using a qubit coupled to a single bosonic mode in a coherent state as a concrete example.

Experimental results

Research questions

• RQ1 How can a thermodynamically consistent master equation be constructed for a driven open quantum system?
• RQ2 What is the role of the drive in ensuring detailed balance and entropy production consistency?
• RQ3 How does the autonomous framework with a control system lead to a semi-classical description of the driven dynamics?
• RQ4 What are the eigenoperators of the driven free evolution, and how do they structure the master equation?
• RQ5 Can the semi-classical limit be consistently derived from an autonomous quantum construction?

Key findings

• The master equation is fully determined by the eigenoperators of the driven free dynamics, ensuring consistency with the system's unitary evolution.
• The thermodynamic postulates—particularly detailed balance and positivity of entropy production—uniquely constrain the form of the master equation.
• The semi-classical limit emerges naturally when the control system is in a coherent state, yielding a time-dependent Hamiltonian for the primary system.
• The framework preserves the physical consistency of thermodynamics even under strong driving.
• The model successfully describes a qubit coupled to a bosonic mode in a coherent state, demonstrating the applicability of the formalism to realistic driven quantum systems.