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  • Open Access

Quasiprobability Thermodynamic Uncertainty Relation

Kohei Yoshimura1,2,* and Ryusuke Hamazaki1,3

  • *Contact author: kohei.yoshimura@riken.jp
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Phys. Rev. Lett. 136, 120406 – Published 27 March, 2026

DOI: https://doi.org/10.1103/ky8n-9bcy

Abstract

We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky–Margenau–Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained inequality plays a complementary role to existing quantum thermodynamic uncertainty relations, focusing on observables’ change rather than exchange of charges through jumps and respecting initial coherence. Quasiprobabilities show anomalous behaviors that are forbidden in classical systems, such as negativity; we reveal that negativity or a nonclassically enhanced escape rate is necessary to increase an output-to-dissipation ratio beyond classical limitations and show that the requirements are basis independent and stronger than quantum coherence. To illustrate these statements, we employ a model that can exhibit a dissipationless heat current, which would be prohibited in classical systems; we construct a state that has much coherence but does not lead to a dissipationless current due to the absence of anomalous behaviors in quasiprobabilities.

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Phys. Rev. Lett. 136, 120406– Published 27 March, 2026
  • Received 19 August 2025
  • Revised 20 February 2026
  • Accepted 26 February 2026
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