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.
Highlights
Consider two systems, C for “cold” and H “hot,” in thermal states at temperatures TC < TH
The situation is less straightforward if the initial state is locally thermal but correlated, since correlations allow for temporary “back flows,” i.e., Q > 0. [2,3]
We show that the associated negative “probabilities” have a clear thermodynamic interpretation as contributions to the heat flows that cannot be explained within the framework of stochastic thermodynamics
Summary
C for “cold” and H “hot,” in thermal states at temperatures TC < TH. Any stochastic interpretation of heat flows that reproduces the observed Q faces severe no-go theorems [5,6] This is the reason why the leading proposal for defining and measuring heat and work fluctuations, the “two-projective-measurement” (TPM), clearly cannot reproduce quantum effects such as strong heat back flows. We show that the associated negative “probabilities” have a clear thermodynamic interpretation as contributions to the heat flows that cannot be explained within the framework of stochastic thermodynamics These quasiprobabilities satisfy an XFT that incorporates quantum correlations in the initial state and includes in the relevant classical limits the original XFT of Ref.
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