Related papers: Heat equation and convolution inequalities
We present a conjugate analysis of two different dark energy models investigating both their agreement with recent data and their thermodynamical properties. The successful match with the data allows to both constrain the model parameters…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
Although its practical efficiency is unquestionable, it is well known that thermodynamics presents conceptual difficulties from the theoretical point of view. It is shown that the problem comes from an imperfect compatibility between the…
In this paper, we prove a differential Harnack inequality for positive solutions of time-dependent heat equations with potentials. We also prove a gradient estimate for the positive solution of the time-dependent heat equation.
Using the contemporary thermodynamic equations of elastic solids leads to contradictions with the fundamental statements of thermodynamics. Two examples are presented to expose the inconsistencies. In example one the internal energy between…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
In recent years a quantum information theoretic framework has emerged for incorporating non-classical phenomena into fluctuation relations. Here we elucidate this framework by exploring deviations from classical fluctuation relations…
This article is a short version of a longer article to appear in Physics Reports (cond-mat/9708200). The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of…
A general discussion is made concerning the ways in which one can get signatures about a possible liquid-gas phase transition in nuclear matter. Microcanonical temperature, heat capacity and second order derivative of the entropy versus…
We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using a weak solution approach by Hasanov, the associated cost functional is…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…
For the heat equation in a bounded domain we give a stability result for a smooth diffusion coefficient. The key ingredients are a global Carleman-type estimate, a Poincar\'e-type estimate and an energy estimate with a single observation…
A statistical-mechanical investigation is performed on Rayleigh-B\'enard convection of a dilute classical gas starting from the Boltzmann equation. We first present a microscopic derivation of basic hydrodynamic equations and an expression…
In this paper, we study the Cauchy problem for a heat equation governed by a mixed local--nonlocal diffusion operator with spatially irregular coefficients. We first establish classical well-posedness in an energy framework for bounded,…
We develop the laws of thermodynamics in terms of general exponential families. By casting learning (log-loss minimization) problems in max-entropy and statistical mechanics terms, we translate thermodynamics results to learning scenarios.…
In this expository work we discuss the asymptotic behaviour of the solutions of the classical heat equation posed in the whole Euclidean space. After an introductory review of the main facts on the existence and properties of solutions, we…
The Brascamp-Lieb inequalities are a generalization of the H\"older, Loomis-Whitney, Young, and Finner inequalities that have found many applications in harmonic analysis and elsewhere. In this paper we introduce an "adjoint" version of…
We define the concept of energy-variational solutions for the Navier--Stokes and Euler equations. The underlying relative energy inequality holds as an equality for classical solutions and if the additional variable vanishes, these…
In the last ten years, a number of ``Conventional Fluctuation Theorems'' have been derived for systems with deterministic or stochastic dynamics, in a transient or in a non-equilibrium stationary state. These theorems gave explicit…
The Borell-Brascamp-Lieb inequality is a classical extension of the Pr\'ekopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The stability of these inequalities has received significant…