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We discuss a generalization of the maximum entropy (ME) principle in which relative Shannon classical entropy may be replaced by relative von Neumann quantum entropy. This yields a broader class of information divergences, or penalty functions, for statistics applications. Constraints on relative quantum entropy enforce prior correlations, such as smoothness, in addition to the convexity, positivity, and extensivity of traditional ME methods. Maximum quantum entropy yields statistical models with a finite number of degrees of freedom, while maximum classical entropy models have an infinite number of degrees of freedom. ME methods may be extended beyond their usual domain of ill-posed inverse problems to new applications such as non-parametric density estimation. The relation of maximum quantum entropy to kernel estimators and the Shannon sampling theorem are discussed. Efficient algorithms for quantum entropy calculations are described. For references, see [34, 35, 38, 60, 65, 87].

Spin glasses and error-correcting codes

Nicolas Sourlas, ENS Paris sourlas@physique.ens.fr

Abstract not available, but see [73, 74J.

Individual open quantum systems

Tim Spiller, HP Labs Bristol ts@hplb.hpl.hp.com

The reduced density operator is the conventional tool used for describing open quantum sys tems, that is systems coupled to an environment such as a heat bath. However, this statistical approach is not the only one on the market. It is possible to describe instead the evolution of an individual system, one member of the ensemble. I motivate such an approach and illustrate it with some simple examples. One nice feature is the emergence of characteristic classical behaviour, such as chaos.

Large deviations and conditional limit theorems

Wayne Sullivan, University College Dublin wsulivan@irlearn.ucd.ie

Abstract not available, but see [49].

Topological Time Series Analysis of a String Experiment and Its Synchronized Model

Nick Tufillaro, Los Alamos National Laboratory nbt@goshawk.lanl.gov

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