In this work, we demonstrate the inappropriateness of the Boltzmann-Gibbs log-formulation of the physical Clausius entropy $S$ in connecting thermodynamics and phase space statistics. To achieve our goal, we study thermodynamically the simple case of ideal gases embedded in a finite heat bath and compare the derived equations with the phase space statistical ones obtained within the canonical ensemble. We then show that the results of the aforementioned approaches contradict to each other even… Expand

Based on the property of extensivity (mathematically, homogeneity of first degree), we derive in a mathematically consistent manner the explicit expressions of the chemical potential and the Clausius… Expand

Identical classical particles are distinguishable. This distinguishability affects the number of ways W a macrostate can be realized on the microlevel, and from the relation S=k ln W leads to a… Expand

Preface 1. Introduction Part I. Fundamentals of Statistical Thermodynamics: 2. Probability and statistics Problem set I. Probability theory and statistical mathematics 3. The statistics of… Expand