A relation of thermodynamic relevance between the superadditivity, concavity and homogeneity properties of real-valued functions

TL;DR

This paper establishes a precise condition linking superadditivity, concavity, and homogeneity in real functions, with implications for thermodynamics, clarifying when two properties imply the third.

Contribution

It provides a necessary and sufficient condition for the Landsberg-Thirring theorem relating three key properties of functions, enhancing understanding in thermodynamics and mathematical analysis.

Findings

Identifies a specific condition linking superadditivity, concavity, and homogeneity.

Clarifies when two properties imply the third in the context of real functions.

Applies theoretical results to statistical thermodynamics models.

Abstract

We provide a necessary and sufficient condition for the validity of the following Landsberg-Thirring theorem: for a real-valued function on a convex set, any two of the properties of superadditivity, concavity and homogeneity implies the third. Applications to statistical thermodynamics, following Thirring and Landsberg, are briefly reviewed.