Three-Toed Sloth

Books to Read While the Algae Grow in Your Fur, July 2026

Attention conservation notice: I have no taste, and only the memory of qualification to opine on thermodynamics. Also, most of my reading this month was done at odd hours and/or while chasing after a pre-schooler, so I am probably less reliable and more grumpy than usual.

S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics

This is a very comprehensive treatise on the state of the subject as of the 1962. (As discussed below, that's fine). The theory considered is basically about small departures from the equilibrium state. The intensive variables / thermodynamic forces (temperature, pressure, chemical potential, electrical potential, etc.) are near their equilibrium values, and the departures from equilibrium lead to fluxes of the extensive variables (flows of heat, of volume displacement, of chemical reactions, of electrical current) which are proportional in magnitude to the distance from equilibrium, the constants of proportionality being "phenomenological coefficients", in symbols (eq. IV.1) \[ J_i = \sum_{k}{L_{ik} X_k} \] with the \( J \)'s being the fluxes (extensive variables per unit time per unit volume); the \( X \)'s being the thermodynamic forces (intensive variables minus their equilibrium values); and the \( L \)'s being the phenomenological coefficients. The entropy production (change in entropy per unit time per unit volume) is bi-linear in the fluxes and forces (eq. III.21 and ch. IV.1): \[ \sigma = \sum_{i}{J_i X_i} = \sum_{i,k}{L_{ik} X_i X_k} \] The second law of thermodynamics now amounts to \( \sigma \geq 0 \), forcing the matrix of phenomenological coefficients to be non-negative definite. Various symmetry arguments put further restrictions on the \( L \) matrix. The authors then work out an extremely comprehensive theory of the resulting dynamics (which can be non-linear for a variety of reasons), including Gaussian stochastic fluctuations, and apply it to a huge range of physical problems, of increasing complexity. Comparisons to experimental data are mostly verbal and/or confined to footnotes, but they are made.

The book mostly aims, successfully, to stay at the level of pure thermodynamics. It does, however, invoke statistical-mechanical considerations, about an underlying microscopic structure to matter, in two places. One, which is extremely important to the whole development, is the "Onsager reciprocity relations" (ch. IV.3 and VIII): if, say, a gradient of chemical potential induces a heat flux (which it may), then a temperature gradient will also induce a chemical-reaction flux, and the two phenomenological coefficients will be equal, \( L_{ik} = L_{ki} \). (I'm glossing over the complications induced [you should pardon the expression] by external magnetic fields, but the book handles all that in detail.) The equality of the coefficients actually follows from the time-reversibility of the microscopic physics, from which the thermodynamic quantities emerge. The other important place where statistical-mechanical considerations show up is in the chapter (IX) on the kinetic theory of gases, showing how, at least sometimes, the phenomenological coefficients can actually be theoretically predicted, and not just experimentally measured.

There are some parts of the sciences where I get the impression that they are just done, not because they are now boring or useless, but because everything important has been worked out and received a settled expression. Linear irreversible thermodynamics strikes me as almost this way: the generation or two from Onsager through Prigogine to Mazur said almost everything worth saying, within their domain. The biggest modification a really modern treatment of these phenomena would make would be to add symmetry breaking and order parameters --- so "really modern" dates to 1975. I realize that my saying this makes it (forgive the expression) thermodynamically inevitable that one reader will inform me of all the groundbreaking work done in linear irreversible thermodynamics in recent years, while another reader explains how the theory is entirely refuted. In the meanwhile, I very much enjoyed revisiting thinking seriously about physics. §

(I browsed this in grad school, and sold my copy during one of my moves. Years later, I got stuck on a project until I came up with a trick I was briefly very proud of; then I realized that "my" trick was actually something I'd read about here, the "progress variables" from chapter X on chemical reactions. On the occasion of actually submitting the blessed paper, about which I hope to say more soon, I read / re-read this whole book from scratch, and I am glad I did, though I will confess I skipped the exercises. One thing I had forgotten since the 1990s was that the authors use a system of notation for matrices and tensors I have literally never seen anywhere else. --- I bought my current copy in 2023 directly from Dover, which at the time threw in an electronic copy for no extra cost. [The e-book is an EPUB with decent but not perfect OCR and no hyperlinks.] I can't tell from their website if they are still doing that.)

Emily Croy Barker, The Thinking Woman's Guide to Real Magic

Mind candy fantasy: in which an early-21st-century American young woman, whose English-lit thesis and love life are going equally poorly, does a good deed; gets rewarded with three wishes, without realizing it; and, in consequence, wanders off, first into Faery and then into a Fantasyland which is convincingly poor, sexist and dirty, but also magical. Drama ensues. §

Ilona Andrews, This Kingdom Will Not Kill Me

Mind candy fantasy: in which an early-21st-century American young woman wakes up in the world of her favorite fantasy series, which is not Game of Thrones, but is also obviously inspired by Martin, and does her best to thrive using her prodigious knowledge of the books. Inevitably, this is something of a commentary on why anyone would want to read such books. §

Scientifiction and Fantastica; Physics