Russell Standish wrote:
On Fri, Nov 07, 2014 at 12:59:28PM +1100, Bruce Kellett wrote:
I agree that the past hypothesis, while it explains the
thermodynamic AoT, itself stands in need of explanation. This is the
great unsolved problem of cosmology -- at least according to many
cosmologists. The initial big bang might be assumed to be in
thermodynaic equilibrium, but that is essentially the same
assumption as the assumption of low entropy. The question remains as
Thermodynamic equilibrium is at maximum entropy.
This leads me into commenting on your post slightly earlier in this
thread - expansion of the universe is coupled to th second law in that
it allows a universe initially at maximum entropy (thermodynaic
equilibrium) to evolve into a universe not at maximum entropy, but
never have entropy decrease, so satisfying the second law.
I think you are making the mistake that Liz made -- you are ignoring the
gravitational degrees of freedom. The quark-gluon plasma of the hot big
bang might have been at thermodynamic equilibrium for the quark and
gluon degrees of freedom, but the gravitational degrees of freedom were
not thermalized. Consequently, the entropy of the plasma was almost
infinitely below the maximum possible. There is no need for the maximum
entropy, whatever that might be, to increase with the expansion because
there is still an enormous potential for entropy to increase as
gravitation comes into play. The time scale for this is much longer than
the timescale of quark processes, so is not evident at early times.
The main role that the expansion plays is in cooling the early universe.
As space expands, relativistic matter cools and non-relativistic matter
simply becomes less dense. Energy is not conserved in these processes.
Neither of these process affect any entropy bound, but they are
essential for the formation of order in the form of bound states, then
clusters of gas, galaxies, stars and so on. All these processes are
according to the standard laws of physics -- all obey the second law and
lead to increases in entropy. But entropy remains many many orders of
magnitude below any possible bound throughout all of this.
The equation is S_max = S+C, where S_max grows as the universe
expands, and S=S_max indicated thermodynamic equlibrium. The value C
indicates complexity, or information content of the universe, and is
the bit we find interesting. I think this is Dewar's equation - but it
may also possibly be attributable to Brillouin, who pointed out that C
could be considered to be Shroedinger's "negentropy".
Because it ignores gravity, this equation cannot be applied to the
universe as a whole.
The point being that we can have both dS/dt > 0 (2nd law) and dC/dt >
0 (evolution of complexity), but only in an expanding universe
dS_max/dt > 0.
Of course complexity can increase while entropy increases. This is
because the universe started in an unusually low entropy state. The
expansion of the universe does not affect any entropy bound. See the
argument by Penrose in 'The Road to Reality', Sect. 26.7 (from memory,
though it may be a nearby section).
Bruce
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