1 Abstract The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Gini-bre RME), are applied to following quantum statistical systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integr...

1 Abstract The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Gini-bre RME), are applied to following quantum statistical systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integr...

For the BTZ black hole in the Einstein gravity, a statistical entropy has been calculated to be equal to the Bekenstein-Hawking entropy. In this paper, its statistical entropy in the higher curvature gravity is calculated and shown to be equal to the one derived by using the Noether charge method. This suggests that the equivalence of the geometrical and statistical entropies of the black hole ...

The Maximum Entropy Modeling Toolkit supports parameter estimation and prediction for statistical language models in the maximum entropy framework. The maximum entropy framework provides a constructive method for obtaining the unique conditional distribution p*(y|x) that satisfies a set of linear constraints and maximizes the conditional entropy H(p|f) with respect to the empirical distribution...

We compute the spectrum of quarter BPS dyons in freely acting ZZ2 and ZZ3 orbifolds of type II string theory compactified on a six dimensional torus. For large charges the result for statistical entropy computed from the degeneracy formula agrees with the corresponding black hole entropy to first non-leading order after taking into account corrections due to the curvature squared terms in the e...

We have presented a new axiomatic derivation of Shannon entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function. We have then modified Shannon entropy to take account of observational uncertainty.The modified entropy reduces, in the limiting case, to the form of Shannon differential entropy. As an application, we have de...

Entanglement entropy is a statistical entropy measuring information loss due to coarse-graining corresponding to a spatial division of a system. In this paper we construct a thermodynamics (entanglement thermodynamics) which includes the entanglement entropy as the entropy variable, for a massless scalar field in Minkowski, Schwarzschild and Reissner-Nordström spacetimes to understand the stati...

In statistical physics, Boltzmann-Shannon entropy provides good understanding for the equilibrium states of a number of phenomena. In statistics, the entropy corresponds to the maximum likelihood method, in which Kullback-Leibler divergence connects Boltzmann-Shannon entropy and the expected log-likelihood function. The maximum likelihood estimation has been supported for the optimal performanc...

Min-entropy is a statistical measure of the amount of randomness that a particular distribution contains. In this paper we investigate the notion of computational min-entropy which is the computational analog of statistical min-entropy. We consider three possible definitions for this notion, and show equivalence and separation results for these definitions in various computational models. We al...