Waiting for a better bound in nonequilibrium thermodynamics

I've been keenly interested in nonequilibrium thermodynamics for a while, ever since graduate school. Originally, my idea for being interested was based on the idea that it provided insight into biology. This is not a bad idea-- the minimal cortical wiring hypothesis says that neural systems minimize cortical wiring while retaining function. Why would they do that? Well, the usual reason is that the brain of the child has to fit through the mother's vagina, but you could also cite timing delays as being costly for computational reasons and also cite energy considerations. And in fact, there is a paper by Hausenstaub that suggests that energy minimization is crucial when deciding what kinds of channel densities and kinetic parameters still produced action potentials in neurons. And I have an unpublished manuscript (still in my advisor Mike DeWeese's hands) that suggests that eye movements are driven by energy considerations ala visuomotor optimization theory reinterpreted-- maybe.

However, I have been somewhat sad at the match between nonequilibrium thermodynamics and biophysics. Basically, the question is this: do Landauer-like bounds matter? A long time ago, Landauer proposed that there was a fundamental limit on the energy efficiency of engineered systems. This limit is far from being obtained. But you might hope that evolved systems have attained this limit, or something like it. There is some evidence that biology is somewhat close to the limit, but the evidence is sparse and could be easily reinterpreted as not being that close. We are about half an order of magnitude off of the actual nonequilibrium thermodynamic bound in bacterial chemotaxis systems, in simple Hill molecule receptors, with a match to an improved nonequilibrium thermodynamic bound being given with networks that I am not sure are biologically realistic. There is a seeming match with Drosophila, which tends to have surprisingly optimal information-theoretic characteristics, and also with chemosensory systems again. I am sure I'm missing many references, and please do leave a comment if you notice a missing reference so I can include it.

This may look promising. To me, it's interesting what we need to do to get rid of the half an order of magnitude mismatch. Now, half an order of magnitude is not much. Our biological models are not sufficiently good that half an order of magnitude means much to me, so the half an order of magnitude basically has error bars the size of half an order of magnitude because we just don't understand biology. But beyond that, we should have more examples of biology meeting nonequilibrium thermodynamic bounds. I think we can get there by incorporating more and more constraints into the bounds. For example, incorporate the modularity of a network, and you get a tighter bound on energy dissipation.

I want to use nonequilibrium thermodynamic bounds in my research, but haven't for a while. I just need better bounds with more constraints incorporated. Does the network you're studying have modularity or some degree distribution? Are there hidden states? Is it trying to do multiple things at once with a performance metric for each, e.g. not just Berg-Purcell extended but Berg-Purcell revisited so that we are trying to not just estimate concentrations but predict something about them as well at the same time? Is the environment fluctuating and memoryful, which was one way in which the Berg-Purcell limit was extended?

I'm going to talk to a real expert on this stuff in a few months and will update this post then to reflect any additional links. Please do comment if there are links I've missed while being out of the field for years. I am quite curious.