Carnot efficiency @ phase transitions?

For some time I have been collecting pieces of evidence that efficient engines at nonvanishing power output might be feasible when the working substance is close to a phase transition, because of the physical fact that there is a lot of so-called “latent heat” by which a small perturbation of the thermodynamic forces (e.g. of the temperature) might give rise to a huge current.

In our PRL on efficiency fluctuations based on a Gaussian model, we noticed that the two peaks of the efficiency p.d.f. both converge to Carnot when the covariance matrix becomes singular, commenting that “it is tempting to parallel this behavior to the paradigm of criticality at phase transitions, where fluctuations become macroscopic, correlations diverge, and the covariance matrix degenerates“.

Another element in this direction come from the analysis of Campisi and Fazio

Campisi, Michele, and Rosario Fazio. “The power of a critical heat engine.” Nature communications 7 (2016).

who noticed that, when the working substance of a quantum Otto cycle consists of N coupled components, in the large-N limit close to a critical point a conspiracy of critical exponents might lead to a super-linear scaling of efficiency versus power. They conclude that “obstacles hindering the realization of the critical powerful Carnot engines appear to be of technological nature, rather than fundamental”.

Now a new piece of evidence comes from this recent manuscript:

Patrick Pietzonka, Udo Seifert, Universal trade-off between power, efficiency and constancy in steady-state heat engines, arXiv:1705.05817

They prove the following relation between efficiency, power, and the power’s scaled variance $\Delta_P$

$\eta_C/\eta \geq 1 + 2T_c P / \Delta_P$

where the Carnot efficiency and the temperature of the cold reservoir appear. What is very interesting here is that, if one wants to maintain a finite efficiency bound, the fluctuations of the power output should be of the same order as the power output itself. Which is precisely one of the basic tenets of phase transitions! This can be seen to be the case in our Gaussian model of efficiency fluctuations, and it calls for the realization of a more explicit model working as an engine and displaying this sort of critical behavior.

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