4 ms·
> How can we reconcile this? We can say that the system is not probabilistic, but it is approximately probabilistic. It is indeed probabilistic based on your e
by Majromax 6y ago
> How can we reconcile this? We can say that the system is not probabilistic, but it is approximately probabilistic.
It is indeed probabilistic based on your existing knowledge of the system. The idea that (say) a roulette wheel evolves according to deterministic laws of physics is not useful to you since you do not know the current micro-state necessary to make the prediction.
This is similar to the difference between frequentist and Bayesian interpretations of statistics. Bayesian statistics is more comfortable taking probability distributions over notional facts (such as 'is this coin unfair/weighted?') because it treats the experimenter's confidence as the fount of probability.
If you treat entropy in the same way, it makes more sense. The entropy of a system is related to the number of microstates it can occupy consistently with our known macrostate (e.g., measurement of temperature and pressure -- inherently averaged quantities).
- deleted 6y ago[deleted]
- im3w1l 6y agoThe issue I have with this is that the system is in a given microstate. We may not know which one, but there is one and exactly one. And it will evolve deterministically from that one. And if we look at how it evolves it may do things that seem very unlikely from a random macro point of view. Assume for instance there is a macrostate with a huge amount of energetically favourable microstates. But our little microstate could be destined never to enter any of them. Typically there is an assumption right, that any state could transition into any state at a probability given only by the energies but that isn't really true.
- jbay808 6y agoGrandparent is right. Entropy is best thought of as a two-parameter function. Not entropy(system), but rather entropy(system, your knowledge of system). The system is in a microstate, but you don't know which one. If you did, it would have zero entropy. Since you only have a few general measurements like "one litre of gas at room temperature and one atmosphere of pressure", the entropy is much higher, because many microstates meet that description. If you think of entropy as an objective property of the system regardless of a given observer's state of knowledge, you'll likely get confused.