Full statistics of energy conservation in two times measurement protocols

Tristan Benoist (1, 2) , Vojkan Jaksic (2) , Annalisa Panati (2, 3, 4) , Yan Pautrat (5) , Claude-Alain Pillet (6, 7, 3, 4)

1 ICQ - Cohérence Quantique (LPT)
2 Department of Mathematics and Statistics [Montréal]
3 CPT - Centre de Physique Théorique - UMR 7332
4 CPT - E8 Dynamique quantique et analyse spectrale
5 LM-Orsay - Laboratoire de Mathématiques d'Orsay
6 CPT - E5 Physique statistique et systèmes complexes
7 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille

The first law of thermodynamics states that the average total energy current between different reservoirs vanishes at large times. In this note we examine this fact at the level of the full statistics of two times measurement protocols also known as the Full Counting Statistics. Under very general conditions, we establish a tight form of the first law asserting that the fluctuations of the total energy current computed from the energy variation distribution are exponentially suppressed in the large time limit. We illustrate this general result using two examples: the Anderson impurity model and a 2D spin lattice model.

Domaines: Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Tristan Benoist, Vojkan Jaksic, Annalisa Panati, Yan Pautrat, Claude-Alain Pillet. Full statistics of energy conservation in two times measurement protocols. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (3), pp.032115. ⟨10.1103/PhysRevE.92.032115⟩. ⟨hal-01137957⟩