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 the 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 proxies of nonclassicality. 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 an arbitrary dimension, is no 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.
- Received 8 October 2019
- Revised 10 July 2020
- Accepted 8 September 2020
DOI:https://doi.org/10.1103/PRXQuantum.1.010309
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Fluctuation theorems are a universal and remarkable way of generalizing the second law of thermodynamics. They go beyond statements about what typically happens by fully incorporating the role of fluctuations, which become increasingly dominant at the microscale.
Yet current fluctuation theorems do not account for important phenomena that occur on a quantum scale. The implications of these quantum phenomena for the study of system fluctuations remain largely unknown. Our article takes on this unexplored terrain. We reveal that fluctuations in the heat exchange between two thermal states can be described by a quasiprobability distribution, i.e. probabilities that can counterintuitively turn negative, which are accessible through weak measurement protocols. In our derivation, negative probabilities indicate the presence of quantum behavior within the heat exchange. Strong heat flows between the two thermal states due to quantum correlations go beyond what we witness in stochastic thermodynamics and become possible only in the presence of negative probabilities.
We map the limits of stochastic thermodynamics through heat flow inequalities. Violations of these inequalities witness negative probabilities and hence indicate the presence of quantum behavior. We show that such violations can be reproduced in realistic experiments, and we analyze recent experimental data that demonstrate our new predictions.
These results establish quasiprobabilities as an important tool for capturing quantum thermodynamic phenomena that have no analogs in stochastic thermodynamics. They also open the possibility of applying the extensive technical tools, based on quasiprobability representations developed in quantum optics and computing, to the field of nonequilibrium thermodynamics.
