Fluctuation-induced current from graphene

Abstract
The conservation laws of linear momentum, and of energy, force the Brownian ripples of a graphene membrane to be accompanied by temperature gradient ripples. Thus the system is driven out of a uniform single temperature state.

P. M. Thibado et. al.^1-2 devise a circuit based on freestanding graphene membranes to harvest energy from a system at a single temperature. They are aware that such a system does not comply with the second law of thermodynamics, for example, the postulate of Lord Kelvin:

"A transformation whose only final result is to transform into work heat extracted from a source which is at the same temperature throughout is impossible" ³.

They claim that the energy may be harvested from fluctuations of the Brownian ripples of the graphene membranes, a process that is assumed to be possible by stochastic thermodynamics ⁴.

Consider the charge carriers in the graphene membrane as particles in a box. Whenever a particle collides with a wall of the box it will bounce back to a different direction but will maintain the same speed. However, if the wall is moving, the particle speed will increase, or decrease, depending on the moving direction of the wall ^{5, 6}. This change of speed is a direct outcome of the laws of conservation of linear momentum and conservation of energy. Collisions with moving walls is the mechanism by which the macroscopic mechanical work of the wall is transformed into thermal heat, or vice versa.

Thus the ripple of the graphene membrane must stimulate the heating of its one face and cooling of its other face. The mechanical ripple of the membrane must be accompanied by a ripple of a temperature gradient and the system is no longer maintained at a single temperature.

In a different document ⁷, says Thibado: "That's an important distinction, because a temperature difference between the graphene and circuit, in a circuit producing power, would contradict the second law of thermodynamics. This means that the second law of thermodynamics is not violated …"

However, the conservation laws of linear momentum and energy tell us that there are additional energy flows in the system, a single temperature is not possible, and the problem with the second law is still there.

References

1. P. M. Thibado, et al., “Fluctuation-induced current from freestanding graphene” Physical Review E 102.4 (2020): 042101.
2. T. Anderson, "Stochastic thermodynamics finds exceptions to the law of entropy", https://medium.com/the-infinite-universe/scientists-are-creating-perpetual-motion-machines-and-the-science-is-legit-e9e17b95dcd5, December 2020.
3. E. Fermi, "Thermodynamics", ch. 3, "The second law of Thermodynamics", (1936), Dover, p. 30, (1956).
4. References in ¹.
5. F. W. Sears, and G. L. Salinger, "Thermodynamics, Kinetic Theory, and Statistical Thermodynamics", 3rd. ed., Addison-Wesley, Reading, Massachusetts, p 262-264 (1975) .
6. U. Lachish, "Particles in a Box", https://urila.tripod.com/particles-in-a-box.pdf, January 2021. .
7. "University of Arkansas, "Physicists build circuit that generates clean, limitless power from graphene"", https://phys.org/news/2020-10-physicists-circuit-limitless-power-graphene.html?fbclid=IwAR0C50I9HyC0o7vEeuJrYLIodMZg7bxW_mK0VWkhznXK0fPXs1YRcUZcVio.

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On the web: January 2021.