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Entropy in the Wolfram model

Posted 5 months ago
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Is there a way to think of entropy in the spatial hypergraph? Or does it correspond to the fact that branches are branching in the multiway graph? I expect there should be a relation between time passing and entropy rising in the model. Once we have this, I am wondering if there would then be a way to represent life in the model if it can be defined as the thing in the universe which feeds off negative entropy or free energy as Schrödinger claimed.

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I think it correspond to the fact that branches are branching in the multiway graph. And if it is so then entropy truly is dimension-less and doesn't matter (because it is completely reversible)

There are many definitions of entropy. In general, the intuitive idea is that the entropy of a macrostate is proportional to the logarithm of the number of microstates consistent with the (macroscopic) properties of this macrostate. Consider an object (macrostate) whose microstates are spatial hypergraphs. Then the entropy of this object, with respect to the Wolfram Model that describes it, is proportional to the logarithm of the number of spatial hypergraphs consistent with the macroscopic properties of this object. For example, in a Wolfram Model of String Theory, the entropy of a given string (macrostate) is proportional to the number of spatial hypergraphs consistent with the properties of this string.

Posted 3 months ago

Thanks for your replies. I have begun to understand entropy a bit more since I posed this question. Stephen himself gives good explanation of entropy in his science Q&A (for 33 year old kids like me) which I will link here which helped me understand that my initial idea was too simplistic - https://youtu.be/1ihCUeCtLCk?t=1519 .

Clearly reversibility and macro vs. micro states are important concepts here. That entropy should always increase in the model is not necessarily true if the level of analysis is down at the level of the atoms of space, not up at the level of particles. So I think to understand the 2nd law of thermodynamics we may have to wait to first understand how topological obstructions result in mass particles.

Now I have a new question which is why should mass particles made of topological obstructions attract to each other in what we call gravity? My initial guess is that it must have to do with how topological obstructions first persist (which is itself perhaps anti-entropic) and second how they both individually and collectively increase the local dimensionality of space relative to the vacuum.

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