lsusr

Is entropy objective or subjective?

DaemonicSigil

In one sense subjective, if you believe in subjective probabilities. i.e. if we use Shannon's entropy formula, $- \sum_{i} p_{i} log p_{i}$ then the formula itself is objective, but Bayesians would have subjective probabilities $p_{i}$ , which might vary from person to person.

On the other hand, it does seem to be the case that there are ways in which entropy is very clearly objective. Like the entropy of a box of gas isn't going to vary from person to person, and it's not possible to avert the heat death of the universe by simply changing your subjective beliefs in such a way that entropy goes down.

It's a strange tension to have in your worldview, that entropy should be both subjective and somehow also not. I have this meme lying around somewhere, let me see if I can pull it up...

"The second law of thermodynamics from various perspectives":

Anyway, the joke is to ask what the second law of thermodynamics looks like for people in various states of knowledge. For us humans, there is much we don't know, we're surrounded gas (and other things) made from atoms bouncing around in ways we haven't observed. And entropy goes up all the time, whenever there is friction, or any other dissipative process. Then, Laplace's demon is a stand-in for what we'd call a "logically omniscient being". The demon isn't all-knowing, but it has infinite memory and computational power. Since the laws of physics are reversible, entropy never increases for such a being. Apparent increases in entropy for us mortals are just the result of probability distributions become too complicated and tangled up for us to track. And then "God" would be a stand in for true omniscience, that actually does know the position of every atom. For God, for whom everything is certain, entropy is 0. (The rest of the meme is just a comment on the fact that Conway's game of life is not reversible, left as exercise for the reader.)

lsusr

You seem not to have fallen for my trick question. Often, the people I talk to assume that entropy is necessarily an objective quantity. After all, $S = entropy$ appears in thermodynamic equations like $d S = \frac{\partial Q}{T}$ . But what I find most interesting about your comment is the phrase "if you believe in subjective probabilities".

Are probabilities subjective? Litany of Tarski.

lsusr

If probabilities are subjective,
I desire to believe that pr

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Dialogues on Rationality