Quantum Fluctuation Relations for the Lindblad Master Equation

Raphael Chetrite (1) , Kirone Mallick (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.

Mots clés: Fluctuation relations; Quantum Markovian process; Fluctuation Dissipation Theorem

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]; Mécanique statistique [cond-mat.stat-mech]

Raphael Chetrite, Kirone Mallick. Quantum Fluctuation Relations for the Lindblad Master Equation. Journal of Statistical Physics, 2012, 148, pp.480-501. ⟨10.1007/s10955-012-0557-z⟩. ⟨hal-00762245⟩