Energy conservation and fluctuation theorem are incompatible for quantum work
Year: 2024
Type: article
Abstract: Characterizing fluctuations of work in coherent quantum systems is notoriously problematic. Here we reveal the ultimate source of the problem by proving that ( A ) energy conservation and ( B ) the Jarzynski fluctuation theorem cannot be observed at the same time. Condition A stipulates that, for any initial state of the system, the measured average work must be equal to the difference of initial and final average energies, and that untouched systems must exchange deterministically zero work. Condition B is only for thermal initial states and encapsulates the second law of thermodynamics. We prove that A and B are incompatible for work measurement schemes that are differentiable functions of the state and satisfy two mild structural constraints. This covers all existing schemes and leaves the theoretical possibility of jointly observing A and B open only for a narrow class of exotic schemes. For the special but important case of state-independent schemes, the situation is much more rigid: we prove that, essentially, only the two-point measurement scheme is compatible with B .
Source: Quantum
Authors: Karen V. Hovhannisyan, Alberto Imparato
Institutions: University of Potsdam, Aarhus University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
Award: G612036157
OpenAlex ID: W4396659530