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>So you think that it's still somehow meaningful to refer to the macrostate "the ball may be black or white" and the associated entropy even if the color of the

>So you think that it's still somehow meaningful to refer to the macrostate "the ball may be black or white" and the associated entropy even if the color of the ball is known. Yes. A probability distribution can still be derived from a series of events EVEN when the outcome of those exact events are known prior to the actual occurrence. I believe this is the frequentist view point as opposed to the bayesian viewpoint. The argument comes down to this as entropy is really just a derivation from probability and the law of large numbers.

kgwgk 4y ago
I would say that - in this particular example - knowing that the ball is white and will remain white for the next 950 years and will then be black for the next 1000 years, etc. makes the macrostate "the ball may be black or white" irrelevant. However, I agree that one can still define the macrostate as if the color was unkown - and make calculations from it. (It's just that I don't see the point - it doesn't seem a good or useful description of the system.)
- deltaonefour 4y ago
  Probability is invariant to the arrow of time. If I can look at a probability distribution from data collected from the past and generate a probability. Why can't I look to the future and do the same thing? Even with knowledge of the future you can still count each event and build up a probability from future data. Think of it this way. Nobody looks at a past event and says that the probability of that past event was 100%. Same with a future event that you already know is going to occur. The probability number is communicating frequency of occurrence along along a large sample size. Probability is ALSO independent of knowledge from the frequentist viewpoint. Entropy is based off of probability so it is based off this concept. Knowledge of a system doesn't suddenly reduce entropy because of this.
  - kgwgk 4y ago
    That's not the only defition of probability - and it's a very limiting one. Statistical mechanics is based on the probability of the physical state now and not on the frequency of physical states over time. Sometimes we can assume an hypothetical infinite time evolution and use averages over that but a) it's just a way of arriving at the averages over ensembles that are really the object of interest, b) the theoretical justification is controversial and in some cases invalid, and c) doesn't make sense at all in non-equilibrium statistical mechanics. Don't be offended, but "Nobody looks at a future event that he already knows is going to occur and says that the probability of that future event is 100%" is a very strange thing to say. Everybody does that! Ask astronomers what's the probability that there is a total solar eclipse in 2024 and they answer 100%, for example.
    - deltaonefour 4y ago
      >Don't be offended, but "Nobody looks at a future event that he already knows is going to occur and says that the probability of that future event is 100%" is a very strange thing to say. Not offended by your words but I am offended by the way you think. Maybe rather then assuming I'm wrong and your superior, why don't you just ask questions and dig deeper into what I'm talking about. Probability is a mathematical concept separate from reality. Like any other mathematical field it has a series of axioms and the theorems built off the axioms are independent of our typical usage of it in applied applications. Just because it's rare for probability to be used on future events that are already known doesn't mean the math doesn't work. We tend to use applied math, specifically probability, to predict events that haven't occurred yet but the actual math behind probability is time invariant. It can be applied to events that have ZERO concept of time. See Ulam spirals. In Ulam spirals prime numbers have higher probability in appearing at certain coordinates. This probability is determined independent of time. WE have deterministic algorithms for calculating ALL primes. Yet we can still write out a probability distribution. Probability still has meaning EVEN when the output is already known. That means I can look at a series of known past events and calculate a probability distribution from there. I can also look at a series of known future events and do the same thing. I can also look at events not involving time like where prime numbers appear on a spiral and calculate a distribution. Just look at the math. All you need are events. English and traditional intuitions around probability are distractions from the actual logic. You used an english sentence to help solidify your point but obviously our arguments are way past surface intuitions and typical applied applications of probability. Look up frequentist and bayesian interpretations of probability. That is the root of our argument. You are arguing for the bayesian side, I am arguing for frequentist.

kgwgk 4y ago

I would say that - in this particular example - knowing that the ball is white and will remain white for the next 950 years and will then be black for the next 1000 years, etc. makes the macrostate "the ball may be black or white" irrelevant. However, I agree that one can still define the macrostate as if the color was unkown - and make calculations from it. (It's just that I don't see the point - it doesn't seem a good or useful description of the system.)

deltaonefour 4y ago
Probability is invariant to the arrow of time. If I can look at a probability distribution from data collected from the past and generate a probability. Why can't I look to the future and do the same thing? Even with knowledge of the future you can still count each event and build up a probability from future data. Think of it this way. Nobody looks at a past event and says that the probability of that past event was 100%. Same with a future event that you already know is going to occur. The probability number is communicating frequency of occurrence along along a large sample size. Probability is ALSO independent of knowledge from the frequentist viewpoint. Entropy is based off of probability so it is based off this concept. Knowledge of a system doesn't suddenly reduce entropy because of this.
- kgwgk 4y ago
  That's not the only defition of probability - and it's a very limiting one. Statistical mechanics is based on the probability of the physical state now and not on the frequency of physical states over time. Sometimes we can assume an hypothetical infinite time evolution and use averages over that but a) it's just a way of arriving at the averages over ensembles that are really the object of interest, b) the theoretical justification is controversial and in some cases invalid, and c) doesn't make sense at all in non-equilibrium statistical mechanics. Don't be offended, but "Nobody looks at a future event that he already knows is going to occur and says that the probability of that future event is 100%" is a very strange thing to say. Everybody does that! Ask astronomers what's the probability that there is a total solar eclipse in 2024 and they answer 100%, for example.
  - deltaonefour 4y ago
    >Don't be offended, but "Nobody looks at a future event that he already knows is going to occur and says that the probability of that future event is 100%" is a very strange thing to say. Not offended by your words but I am offended by the way you think. Maybe rather then assuming I'm wrong and your superior, why don't you just ask questions and dig deeper into what I'm talking about. Probability is a mathematical concept separate from reality. Like any other mathematical field it has a series of axioms and the theorems built off the axioms are independent of our typical usage of it in applied applications. Just because it's rare for probability to be used on future events that are already known doesn't mean the math doesn't work. We tend to use applied math, specifically probability, to predict events that haven't occurred yet but the actual math behind probability is time invariant. It can be applied to events that have ZERO concept of time. See Ulam spirals. In Ulam spirals prime numbers have higher probability in appearing at certain coordinates. This probability is determined independent of time. WE have deterministic algorithms for calculating ALL primes. Yet we can still write out a probability distribution. Probability still has meaning EVEN when the output is already known. That means I can look at a series of known past events and calculate a probability distribution from there. I can also look at a series of known future events and do the same thing. I can also look at events not involving time like where prime numbers appear on a spiral and calculate a distribution. Just look at the math. All you need are events. English and traditional intuitions around probability are distractions from the actual logic. You used an english sentence to help solidify your point but obviously our arguments are way past surface intuitions and typical applied applications of probability. Look up frequentist and bayesian interpretations of probability. That is the root of our argument. You are arguing for the bayesian side, I am arguing for frequentist.