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arXiv · 2609.36408

Dynamical resource theory of time-reversal symmetry breaking

Jisho Miyazaki·Kohdai Kuroiwa·Mio Murao
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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.

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Jisho Miyazaki, Kohdai Kuroiwa, Mio Murao. 2026-09-29. Dynamical resource theory of time-reversal symmetry breaking. https://arxiv.org/abs/2609.36408

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