Thermodynamic entropy requires a coarse graining procedure to be
specified to define it rigorously. Given a physical system, you decide
to describe it in terms of only a few macroscopic variables. So, only a
few bits of information are specified, which means that there are an
astronomically large number of physical states that are compatible with
it.
The entropy is the logarithm of this number of states, more precisely it
is the amount of information that you would need to specify in order to
point out in which physical state the system is actually in (they don't
need to be equally probably, so in general you need to use the Shannon
entropy formula).
Now, entropy increase only refers to the increase in the number of
states that have the same macroscopic properties. E.g. if you do a free
expansion experiment and assume that the system is completely isolated,
then if the system is known to be in one out of Omega states, then after
the free expansion into the larger volume it can only be in one out of
Omega final states.
However, if you ask how many different physical states there are that
have the same macroscopic properties as the system in the final state,
then you get a much larger answer (if the volume doubles then it will
have increased by a factor of 2^N where N is the number of particles in
the system).
This larger number of possible states are not the states the system can
actually be in, they just look the same after you perform a course
graining to extract its macroscopic properties. E.g. under a time
reversal, almost none of them will evolve back to the smaller volume.
But then if you are given such a perfectly isolated system with that
larger volume and you don't know about its history; for all you know, it
could be in one of these larger number of states. Also the moment it
interacts with the environment, that causes perturbations and all these
larger number of states will be in play.
Saibal
On 24-09-2015 18:15, John Clark wrote:
On Thu, Sep 24, 2015 smitra <[email protected]> wrote:
> The laws of physics forbid creating information out of
nothing
If that were true then entropy would be conserved, but the second
law
of thermodynamics insists that it is not and always increases.
Some physicists have tried to use entanglement and some fancy footwork
to get around this problem but I don't find it very convincing.
John K Clark
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