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Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime

Sheikh Parvez Mandal1,*, Mahasweta Pandit1, Khalak Mahadeviya2, Mark T. Mitchison2,3,†, and Javier Prior1,‡

  • *Contact author: sheikhparvez.mandal@um.es
  • †Contact author: mark.mitchison@kcl.ac.uk
  • ‡Contact author: javier.prior@um.es
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Phys. Rev. Research 8, 013321 – Published 25 March, 2026

DOI: https://doi.org/10.1103/8plx-nfvq

Abstract

Heat exchanged between an open quantum system and its environment exhibits fluctuations that carry crucial signatures of the underlying dynamics. Within the well-established two-point measurement scheme, we identify a “heat operator,” whose moments with respect to the vacuum state of a thermofield-doubled Hilbert space correspond to the stochastic moments of the heat exchanged with a bath. This recasts heat statistics as a unitary time evolution problem, which we solve by combining chain-mapped reservoirs with tensor-network propagation. In a multibath setup, all total and bath-resolved heat moments then follow from a single pure state evolution. We employ this approach to compute transient and steady-state heat fluctuations in Ohmic spin-boson models in and out of equilibrium, accessing the challenging low-temperature and long memory time regimes of the environment. In the nonequilibrium case, we show a crossover in the Fano factor from super-Poissonian to nearly Poissonian statistics under strong coupling asymmetry, corresponding to thermal rectification behavior. The method applies to noninteracting (bosonic or fermionic) nonequilibrium environments with arbitrary spectral densities, offering a powerful, nonperturbative framework for understanding heat transfer in open quantum systems.

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Phys. Rev. Research 8, 013321– Published 25 March, 2026
  • Received 12 May 2025
  • Revised 15 December 2025
  • Accepted 2 February 2026
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