Looking for Work in Quantum Thermodynamics

TL;DR

The paper diagnoses the challenge of generalizing classical work to the quantum domain by examining Perarnau-Llobet et al.'s no-go theorem, which argues against a universal measurement-based definition of quantum work that satisfies both unitary energy changes and two-point measurement (TPM) conditions. It reframes the tension as a measurement-problem issue and shows decoherence can yield approximate compatibility (FAPP) while not delivering true universality. It then advocates a trajectory-based, ontologically grounded approach via Bohmian mechanics (and related MIW theories), defining work as $W^M$ through quantum forces along actual trajectories, with a competing energy-based notion $W^E$. The analysis reveals that no single quantum-work concept preserves all classical roles—operational, energetic, and thermodynamic—across all regimes, leading to a fragmented landscape or a foundational approach to define work in quantum thermodynamics. The work concludes that successful generalization will likely require embracing regime-specific notions or a deeper resolution of the quantum measurement problem, rather than a universal, measurement-based definition of quantum work.

Abstract

This paper diagnoses a much-discussed problem in quantum thermodynamics, that of generalizing classical work into the quantum domain. I begin with the no-go theorem of Perarnau-Llobet et al (2017): no universal measurement scheme for quantum work satisfies two intuitive, classically consilient desiderata. I assess this incompatibility as stemming from the measurement problem. Decoherence restores compatibility for all practical purposes, but raises questions about what 'universality' should mean and whether any measurement scheme can be 'universal'. I consider a different standard of universality -- in terms of ontology -- by defining a trajectory-based notion of quantum work using the quantum potential. While this preserves the classical role of work as the integral of forces over distances, and evades the tension of the no-go theorem, consilience fails elsewhere; no single quantum work concept seems capable of preserving all classical features, raising questions for what it takes for successful generalization of the work concept to quantum thermodynamics.