# Entropic Functionals in Quantum Statistical Mechanics

# Entropic Functionals in Quantum Statistical Mechanics

The mathematical theory of non-equilibrium quantum statistical mechanics has developed rapidly in the last decade. The initial developments concerned the theory of non-equilibrium steady states, the entropy production observable, and linear response theory (Green-Kubo formulas, Onsager reciprocity relations) for open systems driven by thermodynamical forces (say temperature differentials). This line of development was a natural direct quantization of the classical theory. In contrast, extensions of the classical fluctuation relations of Evans-Searles and Gallavotti-Cohen to the quantum domain have led to some surprises and novel classes of entropic functionals with somewhat striking mathematical structure and physical interpretation. In this talk I will describe in simple terms the finite time/finite volume theory of entropic fluctuations and outline general research program dealing with entropic fluctuations in non-equilibrium quantum statistical mechanics.