Entropy and its mathematical properties: consequences for thermodynamics

Abstract

In this work, a comprehensive meaning for entropy is provided on the basis of foundations of information theory and statistical thermodynamics. For this purpose, the close relation between missing information and entropy is presented by emphasizing their probabilistic nature. Furthermore, the physical implications of the mathematical properties of the entropy function are exploited using the elementary notions of differential and integral calculus. Particularly, it is evidenced that the usual thermodynamic inequalities found in many textbooks of physical chemistry are direct consequences of the concavity of entropy. The aim of this work is to show that many concepts presented in textbooks of physical chemistry can be obtained in a simple and mathematically clear way. Keywords Entropy Á Statistical thermodynamics Á Information theory Á Concave functions Leading principal minor C p Specific heat at constant pressure C v Specific heat at constant volume a p Coefficient of thermal expansion j T Isothermal compressibility coefficient