Related papers: Kolmogorov--Nagumo Mean Frameworks for Conditional…
In this article we show a $C^{0,\alpha}$-partial regularity result for solutions of a certain class of cross-diffusion systems with entropy structure. Under slightly more stringent conditions on the system, we are able to obtain a…
Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov-Sinai entropy from the setting of amenable groups. Some parts…
Kolmogorov's axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional…
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…
In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter,…
The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems in the continuum. This principle is an important step in the analysis of Markov evolutions and is usually applied for the…
In classical chaotic systems the entropy, averaged over initial phase space distributions, follows an universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the…
We utilize the generalized entropy theory (GET) of glass formation to address one of the most singular and least understood properties of polymer glass-forming liquids in comparison to atomic and small molecule liquids -- the often…
We find, in an intrinsic form, a generalized Rankine-Hugoniot condition with respect to an entropy density that allows to give the proper interpretation to a formula of Vol'pert reducing the entropy condition on a function with bounded…
In this essay I describe some new results of a framework for composite gravity coupled to matter. These include the Bekenstein-Hawking entropy formula, modifications to the low-$\ell$ moments of the CMB power spectrum, and new perspectives…
We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional…
In this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which we call…
The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional…
Traditional measures of entropy, like the Von Neumann entropy, while fundamental in quantum information theory, are insufficient when interpreted as thermodynamic entropy due to their invariance under unitary transformations, which…
We give un upper bound Ent(\Omega, g)<\lambda\ of the diastatic entropy Ent(\Omega, g) of a complex bounded domain (\Omega, g) in terms of the balanced condition (in Donaldson terminology) of the Kaehler metric \lambda g. When (\Omega, g)…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In…
The probabilistic interpretation of the standard Regge-Gribov model with triple pomeron interactions is discussed. It is stated that introduction of probabilities within this model is not unique and depends on what is meant under the…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…