Here is a thought: If we were to enumerate the set of all possible discrete universe states with the same number of bits, some of those can be interpreted as successor states of another, for a computable transition function (aka a set of physical laws).
Our universe seems to be reversible (i.e. each state has one possible predecessor). A reversible indeterministic universe is difficult to construct, because all you must make sure that every state can only be reached from exactly one other state.
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"One possible predecessor" implies no information loss. Consider two particle transitions, A->B and C->D. We know B and D, but in which order? But lets say you constrain it, say based on momentum, and only have one predecessor state. You're still a long way from constructing...
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...an argument that your one path back leads to your entropic big bang. I'm not trying to be difficult here. Either it does or it doesn't back as you assume, and if it does, what constrains it? Beta decay run backwards is determanistic nuclear capture of an electron.
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