Thermodynamics and concentration

TL;DR

This paper demonstrates how the thermal subadditivity of entropy underpins various concentration inequalities, introducing two new inequalities and unifying several existing results across different mathematical contexts.

Contribution

It provides a unified framework based on entropy subadditivity to derive multiple concentration inequalities and introduces two novel inequalities for broader applicability.

Findings

Unified derivation of concentration inequalities from entropy principles

Introduction of two new concentration inequalities

Application to convex Lipschitz functions and random matrices

Abstract

We show that the thermal subadditivity of entropy provides a common basis to derive a strong form of the bounded difference inequality and related results as well as more recent inequalities applicable to convex Lipschitz functions, random symmetric matrices, shortest travelling salesmen paths and weakly self-bounding functions. We also give two new concentration inequalities.