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KL divergence has also been used to generalize the second law of thermodynamics for systems far from equilibrium: https://arxiv.org/abs/1508.02421 https://arxi
by riemannzeta 3y ago
KL divergence has also been used to generalize the second law of thermodynamics for systems far from equilibrium:
https://arxiv.org/abs/1508.02421 https://arxiv.org/abs/1508.02421
And to explain the relationship between the rate of evolution and evolutionary fitness:
https://math.ucr.edu/home/baez/bio_asu/bio_asu_web.pdf https://math.ucr.edu/home/baez/bio_asu/bio_asu_web.pdf
The connection between all of these manifestations of KL divergence is that a system far from equilibrium contains more information (in the Shannon sense) than a system in equilibirum. That "excess information" is what drives fitness within some environment.
- tysam_and 3y agoI'm not sure if I follow the fitness-driving argument. Without an informational sieve of some kind, isn't it just random entropy? In this case, sure, far from equilibrium has more information, but that just means the system has more flexibility to move, not that the system actually inherently contains more information (stored information vs inbound throughput). Unless it's some kind of Nash game, or problem with multiple similarly-deep valleys, I don't see how that would do much more from a fitness perspective other than allow us to effect something approaching an unbiased estimator of the minima density of whatever problem we're working on is. Or...whatever, I'm not quite sure. Anywho, however it is, I'm a bit confused on the last part there.
- riemannzeta 3y agoI will confess that at least the biology work is still somewhat mysterious to me. John Baez used to be active on Twitter. I believe he's still active on Mathstodon now. If you're curious, you might ask him.