Brent: you beautifully describe the *"...**arbitrarily many possible histories and different possible starting points. ..." - *all within human speculation and within the limited 'model' of the - so far - KNOWABLE inventory of our (scientific?) world(view). Entropy (any form of) is part of such. BH or not, which is also part of it. Who knows what we don't know? Agnostically yours JM
On Fri, Nov 14, 2014 at 5:23 PM, meekerdb <[email protected]> wrote: > On 11/14/2014 1:29 PM, John Clark wrote: > > On 13 November 2014 18:57, LizR <[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 > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
