Work-minimizing protocols in driven-dissipative quantum systems: An impulse-ansatz approach

TL;DR

This paper investigates minimal work protocols in driven quantum systems using an impulse-ansatz approach, revealing nearly optimal solutions in non-Markovian regimes and highlighting limitations of Markovian master equations.

Contribution

It introduces an impulse-ansatz method for quantum thermodynamic optimization and demonstrates its effectiveness across various bath parameters.

Findings

Impulse-like protocols are nearly optimal in quantum non-Markovian regimes.

Markovian master equations can fail even at weak coupling.

Fully quantum approaches are necessary for accurate finite-time thermodynamic analysis.

Abstract

The second law of thermodynamics sets a lower bound on the work required to drive a system between thermal equilibrium states, with equality attained in the quasistatic limit. For finite-time processes, part of the extractable work is inevitably dissipated, motivating the search for driving protocols that minimize the work. While classical stochastic systems have been extensively explored, quantum analyses remain limited and often rely on Markovian master equations valid only in the weak-coupling regime. Here, we study minimal work protocols for representative two-level systems coupled to a harmonic-oscillator bath using a numerically exact method. Inspired by known optimal solutions for Brownian oscillators, we introduce an impulse ansatz that incorporates possible boundary impulses and test it across a wide range of bath parameters. We find that impulse-like features remain nearly optimal in the quantum, non-Markovian regime, at short times. We also identify cases in which the widely used Markovian master equation fails even at weak coupling, underscoring the need for fully quantum approaches to finite-time thermodynamic optimization.