You wouldn't be able to distinguish it degraded dna from a well-formed dna molecule in that sense until you had seen what happened to it in the future. There's a whole discussion about hidden states within some macro state so ordinarily in statistical mechanics your hope is that all the microstates within a macrostate not only look at the same but for the most part they will act the same now. That's not exactly true right like within some macrostate of a glass of water there are some individual microstates where suddenly it will the water will heat up except an ice cube will form in the water.

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