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arXiv · 2106.09870

Thermodynamic uncertainty relation for quantum first passage process

Yoshihiko Hasegawa
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Abstract

We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains. We consider first passage processes that stop after a fixed number of jumps, which contrasts with typical quantum Markov chains which end at a fixed time. We obtain bounds for the observables of the first passage processes in quantum Markov chains by the Loschmidt echo, which quantifies the extent of irreversibility in quantum many-body systems. Considering a particular case, we show that the lower bound corresponds to the quantum Fisher information, which plays a fundamental role in uncertainty relations in quantum systems. Moreover, considering classical dynamics, our bound reduces to a thermodynamic uncertainty relation for classical first passage processes.

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Yoshihiko Hasegawa. 2021-06-18. Thermodynamic uncertainty relation for quantum first passage process. https://doi.org/10.1103/physreve.105.044127

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