Laboratoire de Physique Théorique
Toulouse - UMR 5152

Considering two heat baths locally interacting, assuming the interaction potential mean value is uniformly bounded in time, the mean heat current from one bath to the other is asymptotically equal to the heat current in the opposite direction. Namely, the interaction potential energy is negligible when considering the first law of thermodynamics in mean.

For a classical thermodynamical system, the interaction strength controls also the fluctuations of the total heat current. Particularly, if the interaction potential is bounded, the total heat variation is bounded. Then the interaction potential energy is negligible when considering the first law of thermodynamics at a statistical level.

I will present recent results obtained with A. Panati and R. Raquépas on the fluctuations of the total heat variation for quantum thermodynamical systems in the two time measurement protocol framework. We show that due to the non commutation between the interaction potential and the free total Hamiltonian, the total heat fluctuations are not primarily controlled by the interaction strength but by the UV regularisation of the interaction potential, or equivalently by how the transition rates between energy levels in the baths induced by the interaction decrease with the related energy variation. I will particularly present examples of non interacting fermions and bosons for which the fourth moment of the total heat variation is infinite at almost every time. We conclude that even if the interaction potential is bounded, its contribution to the first law of thermodynamics can be non negligible at a statistical level.