Related papers: Thermodynamics and concentration
During the last two decades, concentration inequalities have been the subject of exciting developments in various areas, including convex geometry, functional analysis, statistical physics, high-dimensional statistics, pure and applied…
In the semi-classical limit, the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature / low…
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…
Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…
We review the fundamental properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the…
The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant…
In our recent letter [1] we discussed that thermodynamics is violated in quantum Brownian motion beyond the weak coupling limit. In his comment, Tasaki [2] derives an inequality for the relative entropy and claims, without making any…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lata{\l}a we provide a concentration inequality for non-necessarily Lipschitz functions $f\colon \R^n \to \R$ with bounded…
The relationships between reversible Carnot cycles, the absence of perpetual motion machines and the existence of a non-decreasing, globally unique entropy function forms the starting point of many textbook presentations of the foundations…
The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the…
We prove that when the Aubry set for a Lipschitz continuous potential is a subshift of finite type, then the pressure function converges exponentially fast to its asymptote as the temperature goes to 0. The speed of convergence turns out to…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
At finite temperature the distribution of the total momentum is an observable characterizing the thermal state of a field theory, and its cumulants are related to thermodynamic potentials. In a relativistic system at zero chemical…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
In this short note we derive concentration inequalities for the empirical absolute moments of square symmetric matrices with independent symmetrically distributed +/-1 entries. Most of the previous results of this type are limited to…
Various soft materials share some common features, such as significant entropic effect, large fluctuations, sensitivity to thermodynamic conditions, and mesoscopic characteristic spatial and temporal scales. However, no quantitative…