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.

  • $\begingroup$ Do you mean starting with statmech and then taking ensemble averages to recover the typical, macroscopic thermodynamic quantities? $\endgroup$ – honeste_vivere Jul 24 at 21:02
  • $\begingroup$ @honeste_vivere yes, pretty much. $\endgroup$ – TheoreticalMinimum Jul 25 at 7:21
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    $\begingroup$ I found this to be very helpful in understanding fluid/thermodynamic limits and other ensemble averaging consequences: ui.adsabs.harvard.edu/abs/1979RPPh...42.1937P/abstract $\endgroup$ – honeste_vivere Jul 25 at 22:12
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    $\begingroup$ As my professor says, most of the research or written work is done because we feel the need for it. Maybe you could write up a book based on your requirement by compiling many references from research literature! $\endgroup$ – Ashwin Balaji Jul 28 at 1:05
  • $\begingroup$ @AshwinBalaji I don't think anyone would want to read such a book written by an undergraduate haha $\endgroup$ – TheoreticalMinimum Jul 29 at 11:41

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.

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