Von Neumann's Entropy Does Not Correspond to Thermodynamic Entropy

Abstract

Von Neumann argued by means of a thought experiment involving measurements of spin observables that the quantum mechanical quantity $S_{VN}=-k\mathrm{Tr}\,(\rho \mathrm{log}\,\rho) $ is conceptually equivalent to thermodynamic entropy. We analyze Von Neumann's thought experiment and show that his argument fails.