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- Hacker News
- Stochastic thermodynamics covers this
- I love this stuff. Like the one definition of death being an organism dying is one that starts failing to maintain itself. Maintenance being the essence of being alive. Or in other words creating local order by sourcing energy from the environment and thus increasing entropy outside the organism.
The laws of thermodynamics are so universal and primordial, they even preceed all of fundamental physics. And once you "get them" which is more like accepting them to be universally true, you can use them to evaluate and explain a lot of things. They help you decern reality from magic for instance, or magical thinking. Ideas that would only work if the second law of thermodynamics makes an exception is magic and therefore impossible in this universe.
by emsign - It's funny the author does not go into Karl Friston's Markov Blanket concept in regards to Life
https://www.fil.ion.ucl.ac.uk/~karl/Life%20as%20we%20know%20...
His paper here presents a heuristic proof (and simulations of a primordial soup) suggesting that life—or biological self-organization—is an inevitable and emergent property of any (ergodic) random dynamical system that possesses a Markov blanket
by AIorNot - So how does one calculate the entropy of a Markov Chain? Is it actually specified? If so, it seems buried.
The Markov chain provided as an example has the edge labels swapped (np should be qp and qp should be np). Regardless, what is the entropy of the example provided?
The problem with Markov chains is that states are dependent, so simply cataloguing states now violates the basic entropy calculation as neighboring states are now dependent on each other.
If the Markov chain is ergodic then maybe you can talk about the entropy of the stationary distribution? Then it's just $-\sum p_i lg(p_i)$ of the stationary distribution probabilities?
The article alludes to how entropy evolves. In the context of ergodic Markov chains, this is related to the size of the second eigenvalue?
by abetusk