Lockless algorithms for mere mortals
Lockless algorithms for mere mortals
Posted Jul 30, 2020 1:55 UTC (Thu) by cyphar (subscriber, #110703)In reply to: Lockless algorithms for mere mortals by Wol
Parent article: Lockless algorithms for mere mortals
In thermodynamics, S = kB ln Ω by definition. The term "entropy" is used in many different fields (such as computer science) and can mean different things (such as Shannon entropy), but in thermodynamics it has a specific meaning -- it is a measure of the number of microstates which appear as a single macrostate. Entropy increases because systems tend towards the macrostates which have the most microstates (again, purely because of statistics).
Posted Jul 31, 2020 21:06 UTC (Fri)
by NYKevin (subscriber, #129325)
[Link] (1 responses)
The problem with this argument is that it is time-symmetric. In other words, you can just as easily argue that the present macrostate is more likely to have evolved from past macrostates which had more microstates. Observation tells us that the time-reversed argument is empirically wrong (because we observe entropy increasing as a function of time), which is a bit of a problem because it appears to be symmetric with the (empirically correct) non-reversed argument. The only (obvious) way to break this symmetry is to assert a boundary condition of low entropy at or near the beginning of the universe. This boundary condition, IMHO, is the real mystery: Why did the early universe have such low entropy? I don't think we have a working answer to that question (yet).
Posted Aug 1, 2020 4:11 UTC (Sat)
by ras (subscriber, #33059)
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Actually no, you can't. In the definition of entropy the number of microstates is fixed and you are measuring how many of those microstate arrangements look like a given macro state.
That aside, no one is disputing there is a thermodynamic arrow of time. The argument being made is that all transitions between microstates are reversible, lossless in terms of information and equally likely in both directions. It's possible for that to be true for micro states and yet there be preferred direction for the evolution of macro states. It's not only possible, it's what happens.
It's not only what happens, there is no mystery as to why it happens. For example, take a go board covered with black and white stones and assume we are near blind. If all black stones are on one side of the board and white on the other we can see that, so black/white is a macro state, but the rest of the possible microstate arrangements just look like grey to us, so grey is another macro state. Back/white corresponds to a few micro states where the black and white stores are poorly mixed. I think there are 361! / 181! possible board arrangements or about 10^431. Most of those states will look just grey - a random mixture of black and white. If the pieces are moving randomly, all of the microstates will be equally likely. This means the odds of seeing black/white instead of grey look to be about 1 in 10^245 if you assume 10% can be out of place. [0] If your go board starts in the black / white macro state, then is allowed to evolve through random 100% completely reversible symmetric swaps you will see it change to grey, and stay that way.
That is the thermodynamic arrow of time. Yet it arose from a completely reversible process. Microstates and macro states are both reasonable ways of looking at the system. When we say time is reversible, we are talking about the former.
[0] Caveat: I am deriving the formulas for these probabilities in my head, as I write this. They are almost certainly wrong.
Lockless algorithms for mere mortals
Lockless algorithms for mere mortals