46 research outputs found
Discontinuities in the Maximum-Entropy Inference
We revisit the maximum-entropy inference of the state of a finite-level
quantum system under linear constraints. The constraints are specified by the
expected values of a set of fixed observables. We point out the existence of
discontinuities in this inference method. This is a pure quantum phenomenon
since the maximum-entropy inference is continuous for mutually commuting
observables. The question arises why some sets of observables are distinguished
by a discontinuity in an inference method which is still discussed as a
universal inference method. In this paper we make an example of a discontinuity
and we explain a characterization of the discontinuities in terms of the
openness of the (restricted) linear map that assigns expected values to states.Comment: 8 pages, 3 figures, 32nd International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, Garching, Germany,
15-20 July 201
Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems
Within the abstract framework of dynamical system theory we describe a
general approach to the Transient (or Evans-Searles) and Steady State (or
Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical
mechanics. Our main objective is to display the minimal, model independent
mathematical structure at work behind fluctuation theorems. Besides its
conceptual simplicity, another advantage of our approach is its natural
extension to quantum statistical mechanics which will be presented in a
companion paper. We shall discuss several examples including thermostated
systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric
spaces and Anosov diffeomorphisms.Comment: 72 pages, revised version 12/10/2010, to be published in Nonlinearit
Entropic Fluctuations in Quantum Statistical Mechanics. An Introduction
These lecture notes provide an elementary introduction, within the framework
of finite quantum systems, to recent developments in the theory of entropic
fluctuations