# Gibbs and von Neumann entropy

**Wayne Myrvold**

I will present an argument, which, which takes pretty much the same form in the classical and quantum contexts, for identifying the Gibbs entropy (for the classical case) or von Neumann entropy (for the quantum) as the statistical analog of thermodynamical entropy. This core of this argument is contained already in Gibbs (1902) and in Tolmanâ€™s classic text (1938). The argument involves proving a theorem that can be regarded as the statistical mechanical version of the Second Law of thermodynamics.

Gibbs, J. Willard (1902). Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics. New York: Charles Scribner's Sons.

Tolman, Richard C. (1938). The Principles of Statistical Mechanics. Oxford: The Clarendon Press.