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Entropic fluctuations in \(XY\) chains and reflectionless Jacobi matrices. (English) Zbl 1281.82017

Two of the authors proposed recently a theory of entropic fluctuations in non-equilibrum quantum statistical mechanics, and the main purpose of the present paper is to examine the kinds of results which can be obtained when this theory is applied to the \(XY\) chain, and it deals with entropic functionals. The authors first describe the \(XY\) chain and then they discuss the thermodynamic limit of the confined \(XY\) chain and its entropic functionals by using a finite time Gallavotti-Cohen functional. The obtained results are then tested against the existence of a non-equilibrium steady state.

MSC:

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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