Related papers: Variation entropy: a continuous local generalizati…
A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…
We consider the differential entropy of probability measures absolutely continuous with respect to a given $\sigma$-finite reference measure on an arbitrary measurable space. We state the asymptotic equipartition property in this general…
We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
We outline how discrete analogues of the conservation of potential vorticity may be achieved in Finite Element numerical schemes for a variational system which has the particle relabelling symmetry, typically shallow water equations. We…
We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
This work is devoted to the study of dissipative fluid systems, through the lens of a geometric variational formulation. Building upon previous works extending Hamilton's principle to non-equilibrium thermodynamics, the present method…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…
The purpose of this work is to analyze the mathematical model governing motion of $n$-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state…
The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…
We prove regularity estimates for entropy solutions to scalar conservation laws with a force. Based on the kinetic form of a scalar conservation law, a new decomposition of entropy solutions is introduced, by means of a decomposition in the…
Total variation denoising (TVD) is a classical method for denoising and curve fitting, yet an explicit pointwise description of its fitted values has only recently been established in the mean regression setting by arXiv:2410.03041v4. This…
The space-discrete Total Variation (TV) flow is analyzed using several mode decomposition techniques. In the one-dimensional case, we provide analytic formulations to Dynamic Mode Decomposition (DMD) and to Koopman Mode Decomposition (KMD)…
For random dynamical systems, by summarizing the fundamental properties of Kifer's topological pressure we introduce the concept of random pressure functions, and define Ruelle's metric entropy for invariant measures. Employing the…
Entropic independence is a structural property of measures that underlies modern proofs of functional inequalities, notably (modified) log-Sobolev inequalities, via ``annealing'' or local-to-global schemes. Existing sufficient criteria for…