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The Kolmogorov complexity of a deterministic universe is constant. The Kolmogorov complexity of a nondeterministic universe grows over time. It grows whenever something happens that is not predetermined by its laws of nature. E.g. randomness or free will.

Would it be possible to measure a difference? If the universe's information content grows, does that also increase its energy content?

Edit: By "complexity of a universe" I mean the amount of information required to simulate it up to some point in time.

LinusK
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2 Answers2

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There are several reasons why this question doesn't make sense:

Algorithmic complexity is relative to some language, but you haven't specified one.

The universe is probably infinite, so its information content may be infinite.

The universe is not a classical system, so classical bits aren't a good way of measuring its information content. Qubits would make more sense. For a quantum system, we expect its information content to stay constant, because time evolution is unitary.

user285342
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Would it be possible to measure a difference?

No, if we are talking about the universe in which we live, and not some simple abstract universe. Why not? Because it's really hard to distinguish a good deterministic pseudo-random number generating algorithm from true randomness. And given that we can access only a minuscule portion of the information describing the universe, this task becomes impossible.

If the universe's information content grows, does that also increase its energy content?

No, there is no relation.

ReasonMeThis
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