Signatures of coherent initial ensembles on all work moments

TL;DR

This paper introduces a non-intrusive operational definition of quantum work that captures the thermodynamic effects of initial coherence, revealing how initial quantum superpositions influence work fluctuations and dissipation.

Contribution

It derives an evolution equation for the work's moment generating function that accounts for initial coherence, providing new insights into quantum thermodynamics beyond traditional measurement-based approaches.

Findings

Different initial ensembles with the same density matrix show distinct work fluctuations.

Coherence-less initial ensembles exhibit maximum work fluctuations for monotonic driving.

Initial coherence can serve as a resource for thermodynamic precision without extra work costs.

Abstract

Standard treatments of quantum work using projective energy measurements erase initial coherence and alter the dynamics, thereby failing to capture the thermodynamic effects of coherent superpositions of energy eigenstates in an ensemble of initial states. In this article, we use an operational work definition that is non-intrusive, applying it to the case of a driven dissipative qubit, where the qubit's initial preparation comprises coherent superposition states, while the driving is coherence-less. We derive an evolution equation for the moment generating function for this work, faithfully capturing the thermodynamic signature of coherent superpositions in the initial ensemble. We demonstrate that different initial ensembles that correspond to the same density matrix upon ensemble average, while having the same average work, display different work fluctuations. For monotonic driving, we show that fluctuations are maximum for coherence-less initial ensembles. As an application, we consider quantum bit-erasure in finite time and demonstrate significantly different work statistics for erasing a classical bit of information versus a Haar random initial ensemble. Our results indicate that coherence in the initial ensemble can be utilized as a resource for thermodynamic precision without incurring additional dissipative work costs. We also obtain a generalized fluctuation theorem that establishes a new quantum lower bound on the mean dissipated work. This bound, counterintuitively, is also applicable to a "classical" initial ensemble with the same initial density matrix and is connected to quantum absolute irreversibility.