Clock-work trade-off relation for coherence in quantum thermodynamics

TL;DR

This paper explores the dual nature of quantum coherence in thermodynamics, revealing a tradeoff between a system's ability to perform work and function as a quantum clock, under minimal thermodynamic assumptions.

Contribution

It introduces a novel clock/work tradeoff relation for quantum coherence types, linking quantum thermodynamics with quantum metrology and macroscopicity.

Findings

Internal coherence can exist without deterministic work value.

External coherence relates to quantum clock functionality.

A fundamental tradeoff bounds the combined clock and work resources.

Abstract

In thermodynamics, quantum coherences - superpositions between energy eigenstates - behave in distinctly nonclassical ways. Recently mathematical frameworks have emerged to account for these features and have provided a range of novel insights. Here we describe how thermodynamic coherence splits into two kinds - "internal" coherence that admits an energetic value in terms of thermodynamic work, and "external" coherence that does not have energetic value, but instead corresponds to the functioning of the system as a quantum clock. For the latter form of coherence we provide dynamical constraints that relate to quantum metrology and macroscopicity, while for the former, we show that quantum states exist that have finite internal coherence yet with zero deterministic work value. Finally, under minimal thermodynamic assumptions, we establish a clock/work tradeoff relation between these two types of coherences. This can be viewed as a form of time-energy conjugate relation within quantum thermodynamics that bounds the total maximum of clock and work resources for a given system.