I think with black holes there's a physically natural coarse-graining
defined by the "no-hair theorem" which says that in classical general
relativity, the only distinguishing characteristics of black holes are
mass, charge and angular momentum, they bear no other traces of the
particular configuration of matter that formed them (of course this may
change in quantum gravity, since Hawking radiation might contain
information about what fell into the black hole). So I think a black hole's
entropy would be defined in terms of the number of possible microstates in
quantum gravity compatible with a black hole of a given mass, charge, and
More on the no-hair theorem here:
On Thursday, December 5, 2013, LizR wrote:
> On 5 December 2013 21:53, Alberto G. Corona
> > wrote:
>> I´m very interested in what you question. One of the wonders of life is
>> how a living being select relevant information from the environment for
>> their needs. I think that the aestetic sense is a heavy part of the
>> activity of the mind at the unconscious level. Form recognition is
>> computation intensive. It is also very puzzling for me how accurately
>> people recognize intuitively order or disorder in agreement with what
>> would be the real entropy calculated in physical terms.
>> It seems that the filtering of information that is not relevant and to
>> deal with what is relevant has been one of the main evolutionary pressures.
>> A recognized pattern (for example, a porcelain jar with all its details,
>> can be assimilated to a macrostate in entropic terms. A broken porcelain
>> jar reduced to dust makes it undistinguisable from other jars and also
>> unusable for doing a work. For example to transport water. That is why life
>> needs to use low entropic things that can be recognized as interesting
> The vase is only distinct from the dust when viewed above a certain level
> of "coarse graining" - so how does one assign it entropy? It seems like
> entropy exists at our level, but not at the bottom level of atoms and so
> on. Yet a black hole can be assigned an entropy, and you can't get much
> more fundamental than that. It seems to me that there is something missing
> between the thermodynamic "coarse-grained" idea of entropy and the
> (presumable fundamental level) black hole entropy. How is that possible,
> that the same thing exists in two different ways on two different levels,
> one of which appears to be emergent? (Am I missing something important
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