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We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility related to the hypothesis testing of the arrow of time. Under a suitable chaoticity assumption, we establish a Large Deviation Principle and a Fluctuation Theorem for the EP.
We consider the general physical situation of a quantum system $H_0$ interacting with a chain of exterior systems $bigotimes_N H$, one after the other, during a small interval of time $h$ and following some Hamiltonian $H$ on $H_0 otimes H$. We discu
We develop a martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into an exponen
In this paper, we consider the classical Ising model on the Cayley tree of order k and show the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out that the fou
We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail and a semi-
We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the density functio