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I was thinking of a random process as: a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.

Given, it is non-deterministic it can be achieved only through processes such as symmetry breaking, collapse of the wave function and hence involve an increase in entropy.

Related: Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?

My question is what is the minimum amount of heat involved in creating a random sequence of a particular length?

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