On 11/14/2014 1:29 PM, John Clark wrote:
On 13 November 2014 18:57, LizR <[email protected] <mailto:[email protected]>>
wrote:
> There appears to be a discrepancy between entropy as it is ascribed
to black holes and entropy in the form of
configurations of mass-energy far from thermodynamic equilibrium. Black
hole
entropy appears to be a fundamental feature of physics, while the other
sort
only emerges due to coarse graining. I'd be interested to know if
anyone can
shed any light on this apparent discrepancy.
I'm not sure what you mean that there are 2 types of Entropy, it always works the same
way. The Entropy of a Black Hole (and the Entropy of anything else) is Boltzmann's
constant time the logarithm of the number of ways the Black Hole could have gotten into
the state it's in now. The reason we use a logarithm in the definition is we want to be
able to say that the total Entropy of the combined system X and Y is the Entropy of X
PLUS the Entropy of Y, if we didn't use logarithms it would be X times Y. For example,
if system X could have gotten to the way it is now in 3 different ways and system Y
could have gotten to the way it is now in 5 different ways then the combined system
could have gotten to the way it is now in 3*5 =15 different ways, but ln 3 + ln 5 = ln 15.
Any constant could be used but it is convenient to use Boltzmann's constant because it's
nice if Entropy is in units of energy/temperature.
"The numbers of ways the system could have gotten to the way it is" isn't the usual
formulation and I think it's ambiguous. In general there are arbitrarily many possible
histories and different possible starting points. Boltzmann's formulation was the
logarithm of the numbers of possible states consistent with constraints defining the
system, e.g. its total kinetic energy or its temperature and volume. In the case of a BH
the constraints are its classical defining parameters: mass, angular momentum, and
electric charge. Classically there is no finer grained description, so that's what seems
to make BH entropy more fundamental that the usual thermodynamic system.
Brent
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