Landauer's Principle for Trajectories of Repeated Interaction Systems

Eric P Hanson (1) , Alain Joye (2) , Yan Pautrat (3) , Renaud Raquépas (4)

1 CAM - University of Cambridge [UK]
2 IF - Institut Fourier
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay
4 Department of Mathematics and Statistics [Montréal]

We analyze Landauer’s principle for repeated interaction systems consisting of a reference quantum system S in contact with a environment E consisting of a chain of independent quantum probes. The system S interacts with each probe sequentially, for a given duration, and the Landauer principle relates the energy variation of E and the decrease of entropy of S by the entropy production of the dynamical process. We consider refinements of the Landauer bound at the level of the full statistics (FS) associated to a two-time measurement protocol of, essentially, the energy of E. The emphasis is put on the adiabatic regime where the environment, consisting of T ≫ 1 probes, displays variations of order T−1 between the successive probes, and the measurements take place initially and after T interactions. We prove a large deviations principle and a central limit theorem as T → ∞ for the classical random variable describing the entropy production of the process, with respect to the FS measure. In a special case, related to a detailed balance condition, we obtain an explicit limiting distribution of this random variable without rescaling. At the technical level, we generalize the discrete non-unitary adiabatic theorem of [HJPR17] and analyze the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps.

Domaines: Physique mathématique [math-ph]

Eric P Hanson, Alain Joye, Yan Pautrat, Renaud Raquépas. Landauer's Principle for Trajectories of Repeated Interaction Systems. Annales Henri Poincaré, 2018, 19, pp.1939-1991. ⟨10.1007/s00023-018-0679-1⟩. ⟨hal-01574145⟩