One educated in conservative textbook thermodynamics might be surprised to find that there is a long and venerable history of challenges to the second law of thermodynamics worthy of followup inquiry. The first hint that something was amiss with modern thermodynamics perhaps came in 1953, when Enrico Fermi, John Pasta, Stanislaw Ulam and Mary Tsingou performed discretized simulations of a vibrating string with a nonlinear elasticity (1,2,3,4). This became known as the FPUT experiment or the FPUT problem, after the names of the contributing scientists. In this experiment, it was found that, counter to thermodynamic expectations, when the number of elements in the string was small and when the elements were nonlinearly coupled, the system would not thermalize but rather would undergo periodic recurrence to the initial state (3). It was found that the osscillations could be described as solitons obeying the KDV equation (1), and the symmetries of these solitons enabled the system to avoid ergodicity. 

Here you can see a more modern simulation of the FPUT experiment, courtesy of Wikipedia (1)

For many decades, the FPUT experiment was considered a curiosity, though found to be relevant to experiments involving nanoparticles. It was not a means of extracting energy, but it did show that the assumption of ergodicity might not be valid in all physically realizeable systems.

In the interim, Ilya Prigogine wrote many relevant and well cited papers on nonequilibrium statistical mechanics, but his arguments are sophisticated and I have yet to evaluate the relevance to the present systems of interest in detail - hopefully I can write a followup update later, focused on Prigogine's work once I understand it better. 

Eventually, in 2005 Vladislav Capek and Daniel Sheehan, in their book "Challenges to the Second Law of Thermodynamics", identified some specific statistical mechanical conditions under which deviations from standard thermodynamic behavior were possible (5), providing direction for further experimental investigation. Specifically, they found that statistical mechanical systems with strong quantum mechanical coupling would not necessarily behave in an ergodic manner and that strong coupling can often be found at the surfaces and boundaries of a system. Interestingly, Capek's definition of strong coupling involves non-negligible higher order terms like the second order nonlinearity in the FPUT problem, and due to the discretization of the FPUT problem, it's boundaries are finitely far away, typically a few wavelengths of the principal modes at most just as needed in many of the systems Capek describes, so the findings are in agreement. Moreover, the book mentions that it is well known in biology that receptors couple strongly (by Capek's definition) to the molecules they are meant to interact with via various mechanisms. The importance of behavior at boundaries cannot be understated: strong quantum mechanical coupling becomes very unlikely to happen across large distances, so the two requirements go hand in hand.

In the two decades since the publication of Capek and Sheehan's book, researchers have gleaned further insights into these systems and constructed various devices which demonstrate the concepts involved in practice. The core idea, they realized, was that unusual nonequilibrium steady state systems enabling energy harvesting could be found amongst the set of systems for which the thermodynamic limit is a poor approximation. In practice, this means looking for systems with a small number of particles N, systems where the relevant volume V is small (or equivalently, where the boundaries of the system are nearby), or where the ratio of N to V is variable or tends towards zero or infinity.

Daniel Sheehan subsequently produced an "epicatalytic thermal diode" which when immersed in a single heat bath at above 1200 kelvin spontaneously produced a temperature difference of upwards of 100 Kelvin across a small gap in a thin hydrogen atmosphere with a sufficiently long mean free path, between two appropriately engineered electrodes (6,7,8). And to underscore the physical concept, he followed that up with a room temperature "thermal battery" device (9,10) which is the inspiration for the bipolar membrane devices we demonstrate in the above experiment. Daniel Sheehan continues to explore many other example systems, with the intention of eventually making them physically realizeable (11).

Paul Thibado has noticed energy localization effects similar to the FPUT experiment in graphene monolayers suspended across a gap in a substrate so that it vibrates in response to thermal fluctuations, and has found it possible to harvest thermal motions this way by means of parametric variations in capacitance, using sufficiently fast diodes like MIM diodes, although he tends to speak more conservatively about the implications of these experimental results (12,13,14).

And last but certainly not least, Garrett Moddel has encountered anomalous effects which could be explained by the insights from Capek and Sheehan in MIM diodes next to casimr cavities. In these systems the presence of the Casimr cavity seems to perturb the steady state situation associated with the Seebeck effect, pushing it out of equilibrium to produce a nonequilibrium steady state (15,16,17). It is unclear whether this is truly vacuum energy as Garrett calls it, or simply asymmetric boundary conditions far from the thermodynamic limit which enable energy harvesting, though it seems to me to be the latter.

Many other researchers like Germano D'abramo have proposed other systems which should exhibit energy harvesting accompanied by an apparent decrease in entropy, and are working on physically demonstrating these systems. For those interested in further study, check out The Unlab on Youtube (18) or the literature citing "Challenges to the Second Law of Thermodynamics ; it was a small conference in 2022 attended by big names like Stephen Wolfram. Many of the talks are excellent and the conference demonstrates that quietly, in the background, this subject is of great interest to some of the top scientists in the world.

References:

1. “Fermi–Pasta–Ulam–Tsingou Problem.” In Wikipedia, September 24, 2024. https://en.wikipedia.org/w/index.php?title=Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problem&oldid=1247548040.
2. Dauxois, Thierry. “Fermi, Pasta, Ulam and a Mysterious Lady.” arXiv, January 10, 2008. https://doi.org/10.48550/arXiv.0801.1590.
3. Fermi, E.; Pasta, J.; Ulam, S. (1955). "Studies of Nonlinear Problems" (PDF). Document LA-1940. Los Alamos National Laboratory.
4. Zabusky, N. J., and M. D. Kruskal. “Interaction of ‘Solitons’ in a Collisionless Plasma and the Recurrence of Initial States.” Physical Review Letters 15, no. 6 (August 9, 1965): 240–43. https://doi.org/10.1103/PhysRevLett.15.240.
5. Čápek, Vladislav, and Daniel P. Sheehan. Challenges to the Second Law of Thermodynamics: Theory and Experiment. Dordrecht: Springer Netherlands, 2005. https://doi.org/10.1007/1-4020-3016-9.
6. Sheehan, D. P. “Nonequilibrium Heterogeneous Catalysis in the Long Mean-Free-Path Regime.” Physical Review E 88, no. 3 (September 18, 2013): 032125. https://doi.org/10.1103/PhysRevE.88.032125.
   
7. Sheehan, D. P., T. A. Zawlacki, and W. H. Helmer. “Apparatus for Testing Gas-Surface Reactions for Epicatalysis.” Review of Scientific Instruments 87, no. 7 (July 5, 2016): 074101. https://doi.org/10.1063/1.4954971.
   
8. Sheehan, D. P., and T. M. Welsh. “Epicatalytic Thermal Diode: Harvesting Ambient Thermal Energy.” Sustainable Energy Technologies and Assessments 31 (February 1, 2019): 355–68. https://doi.org/10.1016/j.seta.2018.11.007.
   
9. Sheehan, Daniel. “Concentration Cell Powered by a Chemically Asymmetric Membrane: Theory.” SSRN Scholarly Paper. Rochester, NY: Social Science Research Network, May 17, 2022. https://doi.org/10.2139/ssrn.4112190.
10. “APS -2023 Annual Meeting of the APS Far West Section - Event - Experimental Results of a Thermal Battery.” In Bulletin of the American Physical Society, Vol. Volume 68, Number 9. American Physical Society. Accessed November 29, 2024. https://meetings.aps.org/Meeting/FWS23/Session/K01.32.
11. Sheehan, Daniel P. “Supradegeneracy and the Second Law of Thermodynamics.” Journal of Non-Equilibrium Thermodynamics 45, no. 2 (April 1, 2020): 121–32. https://doi.org/10.1515/jnet-2019-0051.
12. Ackerman, M. L., P. Kumar, M. Neek-Amal, P. M. Thibado, F. M. Peeters, and Surendra Singh. “Anomalous Dynamical Behavior of Freestanding Graphene Membranes.” Physical Review Letters 117, no. 12 (September 13, 2016): 126801. https://doi.org/10.1103/PhysRevLett.117.126801.
13. Thibado, P. M., P. Kumar, Surendra Singh, M. Ruiz-Garcia, A. Lasanta, and L. L. Bonilla. “Fluctuation-Induced Current from Freestanding Graphene.” Physical Review E 102, no. 4 (October 2, 2020): 042101. https://doi.org/10.1103/PhysRevE.102.042101.
14. Xu, P., M. Neek-Amal, S. D. Barber, J. K. Schoelz, M. L. Ackerman, P. M. Thibado, A. Sadeghi, and F. M. Peeters. “Unusual Ultra-Low-Frequency Fluctuations in Freestanding Graphene.” Nature Communications 5, no. 1 (April 28, 2014): 3720. https://doi.org/10.1038/ncomms4720.
15. Moddel, Garret, Ayendra Weerakkody, David Doroski, and Dylan Bartusiak. “Optical-Cavity-Induced Current.” Symmetry 13, no. 3 (March 2021): 517. https://doi.org/10.3390/sym13030517.
16. Moddel, Garret, Ayendra Weerakkody, David Doroski, and Dylan Bartusiak. “Casimir-Cavity-Induced Conductance Changes.” Physical Review Research 3, no. 2 (April 20, 2021): L022007. https://doi.org/10.1103/PhysRevResearch.3.L022007.
17. “Zero-Point Energy: Capturing Evanescence. | EBSCOhost.” Accessed November 29, 2024. https://openurl.ebsco.com/EPDB%3Agcd%3A7%3A14426119/detailv2?sid=ebsco%3Aplink%3Ascholar&id=ebsco%3Agcd%3A159924233&crl=c&link_origin=scholar.google.com.
18. YouTube. “The UnLAB.” Accessed November 30, 2024. https://www.youtube.com/channel/UCqC5Gi5IjSlo4daxyLDWSZQ