About the Correlation and Physical Foundation of Thermodynamic and Information Entropy: \(\Gamma\)-Phase Space and the Impact to the Outer World

Abstract

Although the term "Entropy S” has been introduced to thermodynamics by Clausius already in the 19th century and Boltzmann's genius relation \(S = k_B \ln W\) that relates thermodynamics and statistics dates now back to more than a century, it is still controversially discussed up to present days while it became of increasing interest for the study of atoms and ions in dense and complex environments. The introduction of many different terms like, e.g. thermodynamic entropy, statistical entropy, information entropy, Boltzmann entropy, and many other definitions make it very difficult for students (and also for the non-specialized researcher) to understand, what are the common and different properties. It is the purpose of the present paper, to present an entirely physical approach to entropy and to show, that essentially all different terms and definitions have in fact common basic physical foundations. Based on an approach of statistical mechanics and elementary quantum mechanics we explore the phase space properties of N-particle systems and show, that Boltzmann's logarithmic entropy relation can be derived from physical constraints. Based on these considerations we discover that information is not a separate supplementary quantity but impacts on the outer world in the sense of entropy.