A quasiprobability distribution for heat fluctuations in the quantum regime

TL;DR

This paper introduces a quasiprobability distribution to accurately describe heat fluctuations in quantum systems, capturing quantum correlations and coherence effects that traditional methods overlook.

Contribution

It derives a quantum fluctuation theorem using quasiprobabilities, revealing non-classical effects like negativity linked to quantum contextuality.

Findings

Negativities in the quasiprobability indicate quantum non-classicality.

The derived inequalities can be experimentally tested at any dimension.

Application to experimental data confirms the presence of quantum effects in heat transfer.

Abstract

The standard approach to deriving fluctuation theorems fails to capture the effect of quantum correlation and coherence in the initial state of the system. Here we overcome this difficulty and derive heat exchange fluctuation theorem in the full quantum regime by showing that the energy exchange between two locally thermal states in the presence of initial quantum correlations is faithfully captured by a quasiprobability distribution. Its negativities, being associated with proofs of contextuality, are proxys of non-classicality. We discuss the thermodynamic interpretation of negative probabilities, and provide heat flow inequalities that can only be violated in their presence. Remarkably, testing these fully quantum inequalities, at arbitrary dimension, is not more difficult than testing traditional fluctuation theorems. We test these results on data collected in a recent experiment studying the heat transfer between two qubits, and give examples for the capability of witnessing negative probabilities at higher dimensions.