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Physics
Quantum Physics
Quantum analog of Boltzmann entropy?
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[QUOTE="Demystifier, post: 6865895, member: 61953"] The Boltzmann entropy as they define it is [I]not[/I] constant, because they don't define it as you think they do. They consider a [I]single[/I] microscopic trajectory ##X(t)## in the phase space, not an ensemble of trajectories. At each time ##t## the state is a single point in the phase space, so its volume is zero and the Liouville's theorem is irrelevant. The finite phase-space volumes are introduced in a totally different way: they divide the whole phase space into finite cells, so that each cell corresponds to one [I]possible[/I] mAcroscopic state. A possible mAcroscopic state becomes an [I]actual[/I] mAcroscopic state when the microscopic ##X## actually arrives into that mAcroscopic cell. The actual mAcroscopic state is [I]changed[/I] when the microscopic state ##X## arrives from one mAcroscopic cell to another. The Boltzmann entropy of macroscopic state is defined as (Boltzmann constant times the logarithm of) volume of the cell, so the entropy increases when the ##X## arrives from a smaller cell to a larger one. The size of ##X## is always the same (and is zero), but what changes is which cell is filled with ##X##.(*) (*)A nice analogy is a car in the city. The size of the car is constant and negligible compared to the size of the city. But the car travels through the city, so often arrives from a smaller city district to a larger one. [/QUOTE]
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Quantum Physics
Quantum analog of Boltzmann entropy?
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