In these months my (sparser and sparser) research activity will be accompanied by several different sorts of teaching: to master students, to Ph. D. students, to high school students, to high school teachers, and even to kids!
The latter two audiences are surely the more unusual for an academician, so I’ll collect some thoughts about how I plan these activities and how they turn out to be.
The opportunity to teach to high-school teachers is part of a bigger science communication project on the future of energy that will end with a conference in 2018 in my hometown Mantova. The idea is to get high-school teachers, and through them high-school students, to participate to the conference already prepared on some of the themes, and actually be active part of the organization.
I gave a 6h training course introducing some of the most modern insights on thermodynamics done with Markov processes, in particular I wanted to get to the Fluctuation Theorem, and in so doing I want to give a very “system-theoretic” perspective to thermodynamic systems, and scrap off a lot of myths surrounding thermodynamics. The challenge was particularly interesting because all of these people all had a solid, though diverse, University background, they do teach thermodynamics, but of course they might be a bit rusty. So at the same time I could be a bit more philosophical but also go into a reasonable degree of technical detail.
I decided to leave two take-home messages, one more philosophical and one more mathematical. The philosophical message is that all formulations of the second law that involve some sort of “entropy of the universe” do not make sense and lead to that sort of paradoxes that inform so much lay talk (and can even be found in cosmology). Thermodynamics is about processes occurring to systems that are portions of the universe, not a universe on their own, and abstracting the tools for calculations that we use to characterize irreversibility in such systems, making them idealized absolute concepts, is a dangerous operation. To show this, I had to treat to some extent what it means to be an exact or an inexact differential and why these mysterious inexact differentials show up in thermodynamics. The second take-home message was the Fluctuation Theorem as a generalization of the Second Law of Thermodynamics, and its consequences. I surfed through these themes helping myself with some historical references (on which high-school teachers usually connect better) to the Carnot cycle, to Clausius’s entropy, to the Boltzmann equation, to Einstein’s analysis of Brownian motion, and finally to the fundamentals of the thermodynamics of irreversible processes laid down by such people as Onsager and Prigogine.
Though the course was deemed by most as quite challenging and “high”, I think most people could follow the basic lines of reasoning, at least judging from the very passionate questions I received.