The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of information measures that are useful for the description of complex systems. Examples treated are the Rényi entropy, Tsallis entropy, Abe entropy, Kaniadaki...

The formalism of statistical mechanics can be generalised by starting from more general measures of information than the Shannon entropy and maximising those subject to suitable constraints. We discuss some of the most important examples of information measures that are useful for the description of complex systems. Examples treated are the Rényi entropy, Tsallis entropy, Abe entropy, Kaniadaki...

Entropy methods enable a convenient general approach to providing a probability distribution with partial information. The minimum cross-entropy principle selects the distribution that minimizes the Kullback–Leibler divergence subject to the given constraints. This general principle encompasses a wide variety of distributions, and generalizes other methods that have been proposed independently....

We hypothesise that all electroweak symmetry breaking terms such as fermion masses and the W and Z gauge boson masses arise radiatively from just one explicit symmetry breaking term in the Lagrangian. Our hypothesis is motivated by the lack of experimental support and the lack of predictivity of the standard symmetry breaking scenario. We construct a simple model which illustrates our ideas. We...

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent of strong subadditivity: it is an inequality which is true for any four party quantum state, provid...

We consider the general problem of relative entropy minimization and entropy maximization subject to expectation constraints. We show that the solutions can be represented as members of an exponential family subject to weaker conditions than previously shown, and the representation can be simplified further if an appropriate conjugate prior density is used. As a result, the solutions can be fou...

The possibility of reconciliation between canonical probability distributions obtained from the q-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is investigated into. Canonical probability distributions are constrained by both: (i) the additive duality of generalized statistics and (ii) normal averages expectatio...

Body size of organisms spans 24 orders of magnitude, and metabolic rate and life span present comparable differences across species. This article shows that this variation can be explained in terms of evolutionary entropy, a statistical parameter which characterizes the robustness of a population, and describes the uncertainty in the age of the mother of a randomly chosen newborn. We show that ...

We describe a speedup for training conditional maximum entropy models. The algorithm is a simple variation on Generalized Iterative Scaling, but converges roughly an order of magnitude faster, depending on the number of constraints, and the way speed is measured. Rather than attempting to train all model parameters simultaneously, the algorithm trains them sequentially. The algorithm is easy to...