Energy counting statistics in open quantum systems: a microscopic approach to thermodynamic consistency

Starting from a microscopic system-baths description of the energy counting statistics, we study how the problem of thermodynamic consistency translates from the unitary level to the reduced open system dynamics. In the first part of the talk, we focus on quantum master equations (QMEs) and derive a general condition for a time-local QME to satisfy the first and second law of thermodynamics at the fluctuating level. In this context, we show that the fluctuating second law can be rephrased as a Generalized Quantum Detailed Balance condition (GQDB) i.e. a symmetry of the time-local generators which ensures the validity of the fluctuation theorem. When requiring in addition a strict system-bath energy conservation, the GQDB reduces to the usual notion of detailed balance. In the second part of the talk, we approach the problem of thermodynamic consistency from a different point of view, showing that the validity of the fluctuation theorem can be seen as a symmetry of a modified version of the Keldysh contour. Building on these premises we study the work and heat statistics in the Caldeira - Leggett model with time dependent strong coupling, and we use it as a starting point to approach the problem of thermodynamic consistency in the Zwanzig model both in general and in the markovian limit.