Related papers: Why would multiplicities be log-concave ?
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
As is well known, black hole entropy is proportional to the area of the horizon suggesting a holographic principle wherein all degrees of freedom contributing to the entropy reside on the surface. In this note, we point out that large scale…
This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates inter-scale energy fluxes to statistical irreversibility and information-entropy production. The microscopical reversibility of the…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.
In a recent paper Andrei N. Soklakov explained the foundations of the Lagrangian formulation of classical particle mechanics by means of Kolmogorov complexity. In the present paper we use some of Soklakov ideas in order to derive the second…
We prove that the overpartition function is log-concave for all n>1. The proof is based on Sills Rademacher type series for the overpartition function and inspired by Desalvo and Pak's proof for the partition function.
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
We compare weighted sums of i.i.d. positive random variables according to the usual stochastic order. The main inequalities are derived using majorization techniques under certain log-concavity assumptions. Specifically, let $Y_i$ be i.i.d.…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
In physics, Lie groups represent the algebraic structure that describes symmetry transformations of a given system. Then, the descending Lie algebra of those groups are necessarily real. In most cases, the complexification of those Lie…
We consider a wide class of linear stochastic problems driven off the equilibrium by a multiplicative asymmetric force. The force brakes detailed balance, maintained otherwise, thus producing entropy. The large deviation function of the…
We have discovered that two significant quantities within hard particle systems: the probability of successfully inserting an additional particle at random and the scale distribution function, can be connected by a concise relation. We…
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
An upper bound on the ergodic capacity of {\bf MIMO} channels was introduced recently in arXiv:0903.1952. This upper bound amounts to the maximization on the simplex of some multilinear polynomial $p(\lambda_1,...,\lambda_n)$ with…
I summarize Bagnoli and Bergstrom (2005)'s review on log-concave functions, make several corrections, and augment the discussion with further results that can be useful in obtaining monotone hazard rate. I also provide an application of…
I tentatively suggest that the superposition principle of quantum mechanics is explicable in a mathematically natural way if it is possible to understand probability amplitudes as complex-valued logarithms. This notion is inspired by the…
We show that $h_\infty(X+Y)\leq h_\infty(Z+W)$, where $X, Y$ are independent log-concave random variables, and $Z, W$ are exponential random variables having the same respective $\infty$-R\'enyi entropies. Analogs for integer-valued…
Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on…
We use entropy to link fine-structure constant and cosmological constant. We also link nuclear force and gravity. We step on the fundamentals of consciousness for this new millennium with a scientific approach. Statistical and quantum…