The diffusion-through-membrane case is straightforward. If a membrane dividing two compartments is permeable to some solute more in one direction than in the other, and so a concentration difference between the two compartments is created and maintained,
then we have a Maxwell's demon type action and a violation of the second law of thermodynamics par excellence.
It seems that such asymmetric membranes are commonplace but authors are too prudent and either don't comment the second-law aspects at all or add absurd calming texts (don't bother, brothers and sisters thermodynamicists, your second law is alive and
kicking):
"Diffusion rates through a membrane can be asymmetric, if the diffusing particles are spatially extended and the pores in the membrane have asymmetric structure...In its extreme form, this effect will rapidly seal off flow in one direction through a
membrane, while allowing free flow in the other direction. The system thus relaxes to disequilibrium, with very different densities of the permeable species on each side of the membrane."
https://arxiv.org/ftp/cond-mat/papers/0412/0412626.pdf
"In biological systems, ion transport across the cell membrane is mostly directional, an embodiment of ionic rectification. Unidirectional ion transport is related to an asymmetric biological nanopore structure, in which the ionic flow in one direction
is almost totally suppressed...To realize such extraordinary ion transport properties in technical systems, many nanostructures based on different materials have been fabricated by various techniques, such as asymmetric nanochannels, heterogeneous
membranes, and self-assembled two-dimensional materials. The realization of unidirectional ion transport in these examples involves breaking the symmetry of the geometry, surface charge distribution, chemical composition, or channel wall wettability,
separately or simultaneously. Despite massive efforts in this field, it is still a challenge to replicate the functionality of biological nanopores and push unidirectional ion transport further for applications. One reason is that ionic rectification in
synthetic nanofluidic systems still shows a performance inferior to that of their natural counterparts: The rectification ratio in artificial systems is always on the order of a few hundred while biological systems almost completely suppress the ion
diffusion in one direction."
https://www.nature.com/articles/s41467-021-24947-3
"Concentration difference is generated internally by a chemically-asymmetric membrane that drives anisotropic diffusion of electrolyte ions, rather than being provided by an external source...This behavior is thermodynamically intriguing. The repeated
reversion from pH = 0.00 to pH = - 0.01 indicates a spontaneous sorting of hydrogen ions from a maximum entropy state – one in which [H+] is the same in both chambers – to a lower entropy state, one in which they are 2% different. On its face, this
spontaneous reduction in entropy without work input seems at odds with traditional understandings of entropy and the second law [25] but, of course, there is actually no conflict when the entropy changes associated with the walls and membrane are
combined with those of the solutions...The pHs and the resultant electrical power appear to be derived from the thermal diffusion of hydrogen ions, hence from purely thermal energy. At first glance this seems at odds with the second law of thermodynamics;
however, as specified by the cell half-reactions, the anode continuously grows (precipitating AgCl) at the expense of the cathode, which will eventually disappear and bring the AMCC to a halt. Further investigation of AMCC thermodynamics seems warranted.
"
https://www.sciencedirect.com/science/article/pii/S2213138822002466#b0005
Pentcho Valev
https://twitter.com/pentcho_valev
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