Heat Conservation and Fluctuations Between Quantum Reservoirs in the Two-Time Measurement Picture

Tristan Benoist (1) , Annalisa Panati (2, 3) , Yan Pautrat (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CPT - E8 Dynamique quantique et analyse spectrale
3 CPT - Centre de Physique Théorique - UMR 7332
4 LMO - Laboratoire de Mathématiques d'Orsay

This work concerns the statistics of the Two-Time Measurement definition of heat variation in each reservoir of a thermodynamic quantum system. We study the cumulant generating function of the heat flows in the thermodynamic and large-time limits. It is well-known that, if the system is time-reversal invariant, this cumulant generating function satisfies the celebrated Evans–Searles symmetry. We show in addition that, under appropriate ultraviolet regularity assumptions on the local interaction between the reservoirs, it satisfies a translation-invariance property, as proposed in Andrieux et al. (in New J Phys 11(4):043014, 2009). We particularly fix some proofs of the latter article where the ultraviolet condition was not mentioned. We detail how these two symmetries lead respectively to fluctuation relations and a statistical refinement of heat conservation for isolated thermodynamic quantum systems. As in Andrieux et al. (in New J Phys 11(4):043014, 2009), we recover the fluctuation–dissipation theorem in the linear response theory, short of Green–Kubo relations. We illustrate the general theory on a number of canonical models.

Mots clés: Fluctuation relations; Fluctuation–dissipation theorem; Two-time measurement; Quantum thermodynamics

Domaines: Physique mathématique [math-ph]

Tristan Benoist, Annalisa Panati, Yan Pautrat. Heat Conservation and Fluctuations Between Quantum Reservoirs in the Two-Time Measurement Picture. Journal of Statistical Physics, 2020, 178 (4), pp.893-925. ⟨10.1007/s10955-019-02468-0⟩. ⟨hal-01959361⟩