Comprehensive collections of solved problems in thermodynamics and statistical physics are often organized into two distinct parts: macroscopic thermodynamics and microscopic statistical mechanics
He found the PDF version first on a flickering terminal in the basement. It was a digital ghost of a book published in 1974. As he scrolled, the elegance of the solutions began to unfold. Helmholtz free energy: (F = -kT \ln Z
by Daniel Arovas covering information entropy, ensembles, and state configurations. Oxford University Problem Sets : Multiple sets from the Oxford Theoretical Physics by Daniel Arovas covering information entropy
Single-particle partition function: (z = e^\beta \mu B + e^-\beta \mu B = 2\cosh(\beta \mu B)). (N)-particle: (Z = z^N). Helmholtz free energy: (F = -kT \ln Z = -NkT \ln(2\cosh(\beta \mu B))). Magnetization: (M = -\partial F/\partial B = N\mu \tanh(\beta \mu B)). Entropy: (S = -\partial F/\partial T = Nk[\ln(2\cosh(x)) - x \tanh(x)]) where (x = \mu B/(kT)). Heat capacity: (C_B = T \partial S/\partial T = Nk x^2 \textsech^2(x)). (The PDF would then plot these functions and discuss the Schottky anomaly.) Helmholtz free energy: (F = -kT \ln Z
Problems and Solutions on Thermodynamics and Statistical Mechanics (Edited by Yung-Kuo Lim)