8 ms·
It’s probably been 15 years since I looked in detail at a formal treatment of statistical mechanics, so maybe this is well-trodden territory, but... has anyone
by taliesinb 6y ago
It’s probably been 15 years since I looked in detail at a formal treatment of statistical mechanics, so maybe this is well-trodden territory, but... has anyone formalized the idea that the second law can be interpreted as a general inability of computer programs to predict one another? I’m also channeling Wolfram here, but I’m not sure if he ever expressed it exactly this way. But the thing I’m imagining would be: set up some (preferably discrete) dynamical system, and then another different kind of system that you fit variationally to the first. The claim would be that the mutual information between state variables of the second and the first will always gradually decrease — unless they are the exactly the same family, in which case the fit rediscovers the exact dynamics and the two systems are identical. So intuitively, the second law would correspond to the claim that different families of programs cannot accurately simulate each other for very long. In the special case of a coarse graining, this should give you the more familiar story about entropy and the ‘gap’ between macrostates and microstates, but the real story is a more general one than that and is an empirical fact about the “computational universe”, with physics a special case.
- zrm 6y ago> has anyone formalized the idea that the second law can be interpreted as a general inability of computer programs to predict one another? This sounds like the halting problem.
- petermcneeley 6y agoWolfram's "computational irreducibility" is basically the halting problem for physics.
- ssivark 6y agoSounds reminiscent of the data processing inequality https://en.wikipedia.org/wiki/Data_processing_inequality https://en.wikipedia.org/wiki/Data_processing_inequality
- flubert 6y ago>has anyone formalized the idea that the second law can be interpreted as a general inability of computer programs to predict one another? Arieh Ben Naim thinks entropy is better described by Shannon's Measure of Information. I haven't actually read any of his books, but I've been meaning to "one of these days". http://ariehbennaim.com/books/index.html http://ariehbennaim.com/books/index.html
- taliesinb 6y agoFrustrating, that list contains almost no usable links. Its as if he doesn’t want you to actually read or understand what he is saying.
- flubert 6y ago- Entropy Demystified: The Second Law Reduced To Plain Common Sense (https://www.amazon.com/Entropy-Demystified-Second-Reduced-Common/dp/9813100125/ https://www.amazon.com/Entropy-Demystified-Second-Reduced-Co...) - A Farewell to Entropy (https://www.amazon.com/Farewell-Entropy-Statistical-Thermodynamics-Information/dp/9812707077 https://www.amazon.com/Farewell-Entropy-Statistical-Thermody...) - Discover Entropy and the Second Law (https://www.amazon.com/Discover-Entropy-Second-Law-Thermodynamics/dp/9814299758/ https://www.amazon.com/Discover-Entropy-Second-Law-Thermodyn...) - Entropy And The Second Law: Interpretation And Misss-Interpretationsss (https://www.amazon.com/Entropy-Second-Law-Interpretation-Misss-Interpretationsss/dp/981437489X/ https://www.amazon.com/Entropy-Second-Law-Interpretation-Mis...) - Information, Entropy, Life and the Universe (https://www.amazon.com/Information-Entropy-Life-Universe-What/dp/9814651672/ https://www.amazon.com/Information-Entropy-Life-Universe-Wha...) - Entropy: The Truth, The Whole Truth, And Nothing But The Truth (https://www.amazon.com/Entropy-Truth-Whole-Nothing-But/dp/9813147679/ https://www.amazon.com/Entropy-Truth-Whole-Nothing-But/dp/98...) - Four Laws That Do Not Drive The Universe, The: Elements Of Thermodynamics For The Curious And Intelligent (https://www.amazon.com/Four-Laws-That-Drive-Universe/dp/9813223480/ https://www.amazon.com/Four-Laws-That-Drive-Universe/dp/9813...) - TIME'S ARROW (?): The Timeless Nature of Entropy and the Second Law of Thermodynamics (https://www.amazon.com/TIMES-ARROW-Timeless-Entropy-Thermodynamics/dp/1483486869/ https://www.amazon.com/TIMES-ARROW-Timeless-Entropy-Thermody...) - Entropy for Smart Kids and their Curious Parents (https://www.amazon.com/Entropy-Smart-their-Curious-Parents/dp/1527532534/ https://www.amazon.com/Entropy-Smart-their-Curious-Parents/d...)
- adeledeweylopez 6y agoYeah! You can derive the second law from "conservation of information". This is a great resource about thermodynamics which goes into some of these ideas: http://www.av8n.com/physics/thermo http://www.av8n.com/physics/thermo
- taliesinb 6y agoHey Adele! Thanks for the resource. Here's something a bit wilder I'm still trying to wrap my head around: https://www.sciencedirect.com/science/article/abs/pii/S0925231205001165 https://www.sciencedirect.com/science/article/abs/pii/S09252...