Curious45
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Nugatory said:Entropy has a precise mathematical definition. Use that definition, and you'll find yourself agreeing with DaleSpam.
It can do. The 2nd law itself is not this, the mathematic defination is quantum statistical mechanics attempt to explain the law, but it is not the law in itself.
The "arrow of time" stuff is about using that definition of entropy to explain why some physical processes (a swinging pendulum, for example) can be played backwards to get back to the initial conditions; while others (the eggs are broken, beaten with a fork, poured into the omelet pan, cooked, and eaten) cannot.
The pendulum, as a whole, "closed or isolated" system, cannot be "played backwards", because the energy spent has been equalised already (the kinetic energy, tranformed from the chemical energy we eat for example, if you push it with your hands, or wind up a mechanism has already been equalised)
The constantly swinging pendulum, in any given state, does not tell us how much time has passed, if any, if we encounter it for the first time, or look at it in totally random intervals, unless we carefully track the energy and motion expended/equalized (for example via the clock face).
I don't think the thermodynamic arrow of time is "an explanation". It's something we observe about time, that it runs "forwards" not "backwards" which can be defined precisely by the 2nd law. In that sense, it seems to be more of a feature.
Statistical mechanics offer no actual explanation for why the arrow exists in the direction it functions in, it attempts to explain the 2nd law within time, not the arrow of time itself.
I have heard an explanation of why the arrow runs forward, but its outside the scope of this forum.
Keep in mind, the 2nd law is supposed to apply only to closed or isolated systems. We can't define something that interacts with something else, as being closed or isolated on its own. Mathematical or conceptual abstractions might be misleading here.
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