Related papers: Maximum entropy principle and power-law tailed dis…
Regardless of studies and debates over a century, the statistical origin of the second law of thermodynamics still remains illusive. One essential obstacle is the lack of a proper theoretical formalism for non-equilibrium entropy. Here I…
With use of the Second Inverse Maximum Entropy Principle we find entropy functions for systems with fractal distribution functions with order parameter $q$. We compare these entropy functions with those given by the Bose-Einstein and…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving strong space-time entanglement. Its generalization based on nonadditive $q$-entropies…
Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
The paper examines relationships between the conditional Shannon entropy and the expectation of $\ell_{\alpha}$-norm for joint probability distributions. More precisely, we investigate the tight bounds of the expectation of…
The $q$-sum $x \oplus_q y \equiv x+y+(1-q) xy$ ($x \oplus_1 y=x+y$) and the $q$-product $x\otimes_q y \equiv [x^{1-q} +y^{1-q}-1]^{\frac{1}{1-q}}$ ($x\otimes_1 y=x y$) emerge naturally within nonextensive statistical mechanics. We show here…
We prove that information-theoretic maximum entropy (MaxEnt) approach to canonical ensemble is mathematically equivalent to the classic approach of Boltzmann, Gibbs and Darwin-Fowler. The two approaches, however, "interpret" a same…
We show how generalized Gibbs-Shannon entropies can provide new insights on the statistical properties of texts. The universal distribution of word frequencies (Zipf's law) implies that the generalized entropies, computed at the word level,…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
An "entropy increasing to the maximum" result analogous to the entropic central limit theorem (Barron 1986; Artstein et al. 2004) is obtained in the discrete setting. This involves the thinning operation and a Poisson limit. Monotonic…
Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), is extended in two directions. First,…