Dynamical resource theory of time-reversal symmetry breaking

Abstract:Time-reversal symmetry and its violation (T-violation) are fundamental across diverse physics domains, from particle physics to fluctuation theorems and reciprocity. While time-reversal symmetry for isolated systems is simply determined by the Hamiltonian, quantifying the magnitude of T-violation, especially in noisy quantum processes, has been a subject of ongoing debate. Here, we propose an operationally meaningful framework to quantify the intrinsic T-violation of quantum channels. We integrate operationally defined time-reversal transformations into dynamical resource theory to formulate T-violation as a resource. T-violation decomposes into two distinct components: kinematic T-violation originating from antiunitary motion-reversal, and nonunitality driven purely by thermodynamics. This decomposition resolves the longstanding confusion between broken time-reversal symmetry and non-invertibility. Finally, we analyze the resulting resource theory of kinematic T-violation, showing that it is neither quality-like nor quantity-like, and proving the existence of a universal golden unit even within classical channels.

24 pages, 5 figures, 1 table. Comments are welcome

arXiv:2609.36408 [quant-ph]

(or arXiv:2609.36408v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.36408 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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