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Owen Lynch (Nov 22 2021 at 20:48):I am reading Schnakenberg's book on network thermodynamics in biology, and he makes a very interesting and possibly relevant point.
He claims that the use of thermodynamics is not to predict what will happen in a given system, but rather to predict what cannot happen.
So rather than looking for dynamical models of non-equilibrium thermodynamics, we should be thinking about "black-boxing" a variety of systems into thermodynamical systems, and then only constraining their large scale behavior based on this coarse-graining, rather than totally predicting the large-scale behavior.
John Baez (Nov 22 2021 at 21:36):He claims that the use of thermodynamics is not to predict what will happen in a given system, but rather to predict what cannot happen.
That attitude seems to describe a certain kind of thermodynamics. For example in modern "stochastic thermodynamics" there are rules like the Jarzynski equality that make predictions about what will happen.
John Baez (Nov 22 2021 at 21:37):Schnakenberg may have written before that... but still, the Onsager reciprocity relations, and Maxwell relations, are pretty old - and they make predictions about what you see.
Owen Lynch (Nov 22 2021 at 21:47):Yeah, this is definitely in a specific context, i.e. the context of biological systems. In context, he means that for biological systems it is hopeless to derive large-scale behavior from consideration of the complex inner workings of a system, rather one should constrain ones expectations of large-scale behavior by thermodynamics, and then experiment to find out the actual behavior among the behaviors allowed by thermodynamics.
John Baez (Nov 23 2021 at 17:53):Okay. That makes sense. There's been some new work that claims to puts bound on the entropy production of a cow, using only macroscopic features of the cow:
This article is a popularization of the actual work. The actual work uses Schnakenburg's ideas plus coarse-graining. I'd like to understand it!
Owen Lynch (Nov 23 2021 at 18:37):Neat!!
Robin Piedeleu (Nov 24 2021 at 10:35):"The duo shows that the entropic cost of maintaining a heart’s beating time decreases roughly linearly with increasing variance in the normalized waiting time distribution of the beats" - this quotation reminded me of this article on the relationship between clock accuracy and entropy production. I first read about it in this Quanta article. Seems like there's a connection
John Baez (Nov 24 2021 at 17:41):Thanks for pointing that out, Robin! The paper in the Quanta article is this:
John Baez (Nov 24 2021 at 17:43):I haven't looked at it yet, but it sounds more quantum-mechanical. There could be a relation, though!
There's also nice time-energy uncertainty principle in quantum mechanics, which is a bit tricky to state since there's no "time observable"... but you can, after all, state it rather nicely:
John Baez (Nov 24 2021 at 17:43):But this is not about entropy...
Owen Lynch (Nov 24 2021 at 21:36):(warning: I don't know what I'm talking about) In relativistic quantum mechanics, position is still an operator, correct? Given that we don't have a strong distinction between space and time in the relativistic setting, why is position an operator and not time?
Owen Lynch (Nov 24 2021 at 21:37):I should have read the whole post before saying that!
John Baez (Nov 24 2021 at 22:53):Owen Lynch said:
(warning: I don't know what I'm talking about) In relativistic quantum mechanics, position is still an operator, correct? Given that we don't have a strong distinction between space and time in the relativistic setting, why is position an operator and not time?
I think the post explains why there can't be a time operator if energy is bounded below.
There's a kind of position operator in the relativistic quantum mechanics of a single particle, but it behaves a bit funny. Very soon, when you do relativistic quantum mechanics, you start wanting to switch to quantum field theory, which has no position operator (or at least not a good enough one to bother with).
John Baez (Nov 24 2021 at 23:53):I can be more specific: instead of just saying "it behaves a bit funny", it would be better here to focus on this:
There's a position operator, but it doesn't transform the way you'd expect, or any nice way at all, under Lorentz transformations!
So, you can't cleverly use the position operator and Lorentz transformations to cook up some "time operator".
John Baez (Nov 24 2021 at 23:56):(In plain old special relativity, if you know the coordinate of a spacetime point in enough different inertial frames (= inertial coordinate systems), you can figure out its coordinate, using the formula for Lorentz transformations. But that trick doesn't work for the rather crappy position operator in relativistic quantum mechanics!