Physics Asked on August 30, 2021
I would like to read a book which rigorously defines what in applied thermodynamics is called "heat" and gives a proper derivation of the laws of thermodynamics from quantum statistics and the principle of Von Neumann entropy maximization.
I do not want a book which covers thermodynamics and then a bit of statistical physics, but the other way around. It should be on the same level of rigor as for example a graduate course on quantum mechanics would be.
Part II of my online book
A. Neumaier and D. Westra, Classical and Quantum Mechanics via Lie algebras (2011 version)
does precisely that. While it starts off with a chapter giving an axiomatic treatment of phenomenological thermodynamic, the next three chapters rederive all formulas (including the three laws of thermodynamics) in a rigorous way from quantum statistical mechanics, with properly formulated theorems and proofs.
As background one needs a good knowledge of linear algebra and of linear operators in Hilbert spaces, and a basic understanding of quantum mechanics. All statistical mechanics needed is developed from scratch.
Correct answer by Arnold Neumaier on August 30, 2021
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