Quasiprobability Thermodynamic Uncertainty Relation

TL;DR

This paper introduces a quantum thermodynamic uncertainty relation using quasiprobabilities, revealing conditions like negativity necessary for surpassing classical limits and illustrating these with a dissipationless heat current model.

Contribution

It presents a quantum extension of the thermodynamic uncertainty relation based on quasiprobabilities, highlighting non-classical behaviors like negativity and their thermodynamic implications.

Findings

Negativity in quasiprobabilities is necessary for enhanced output-to-dissipation ratios.

A dissipationless heat current can exist in quantum systems without classical analogs.

Non-classical behaviors are basis-independent and stronger than quantum coherence.

Abstract

We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky-Margenau-Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained inequality plays a complementary role to existing quantum thermodynamic uncertainty relations, focusing on observables' change rather than exchange of charges through jumps and respecting initial coherence. Quasiprobabilities show anomalous behaviors that are forbidden in classical systems, such as negativity; we reveal that negativity or a non-classically enhanced escape rate is necessary to increase an output-to-dissipation ratio beyond classical limitations and show that the requirements are basis-independent and stronger than quantum coherence. To illustrate these statements, we employ a model that can exhibit a dissipationless heat current, which would be prohibited in classical systems; we construct a state that has much coherence but does not lead to a dissipationless current due to the absence of anomalous behaviors in quasiprobabilities.