The Fundamental Concepts of Classical Equilibrium Statistical Mechanics

TL;DR

This paper critically examines foundational concepts in classical equilibrium statistical mechanics, exploring the interplay of physical and mathematical aspects, especially probability theory, to clarify the discipline's origins and structure.

Contribution

It provides a detailed conceptual analysis of classical equilibrium statistical mechanics, highlighting the role of probability and setting the stage for non-equilibrium studies.

Findings

Clarifies the conceptual foundations of equilibrium statistical mechanics

Highlights the importance of probability theory in the discipline

Prepares for discussions on non-equilibrium statistical mechanics

Abstract

A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between physical and mathematical aspects, particularly regarding the role of probability theory. The focus is on the equilibrium case, which is currently better understood, serving also as a prelude for a further discussion of non-equilibrium statistical mechanics.