Embedded Agents are Quines

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I don't remember exactly where, but Eliezer wrote about that view of Entropy in the Quantum Physics Sequence.

while probabilities can be subjective, the laws of probability, the rules governing how probability can be manipulated are immutable.

And he wrote about this view of probability in Probability is Subjectively Objective.

It turns out that the Second Law of Thermodynamics is a special case of a more general result called Noether's Theorem, which tells us that a differentiable symmetry of a system with conservative forces automatically generates/has it's own conservation law, and the conservation of energy/the Second Law is a special case of this when the symmetry is time.

Here, a symmetry is a situation where a feature is preserved under transformations, and the fact that physics is time-symmetric, meaning that it doesn't matter whether an identical physical process happens now, in the past, or in the future means that the Second Law of Thermodynamics/Conservation of Energy automatically pops out.

It is not a probabilistic statement, as long as we accept time-symmetry.

https://en.wikipedia.org/wiki/Noether's_theorem

There is another derivation of the Second Law that is more specific to quantum mechanics, and this is also explanatory, but it's pretty specific to our universe:

https://www.quantamagazine.org/physicists-trace-the-rise-in-entropy-to-quantum-information-20220526/

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and the conservation of energy/the Second Law is a special case of this when the symmetry is time

Conservation of energy is not the same thing as the second law of thermodynamics.