"By way of analogy, you know that different observers
report different values of "the" kinetic energy
(depending on the velocity of the observer), and
this hasn't caused the world to end.
3) For macroscopic systems (10^23 particles or
thereabouts) it is uncommon for one observer
to know 10^23 things that the other observer
doesn't ... but even this is possible. The spin
echo experiment is a celebrated example."
I think the analogy between entropy and kinetic energy is superfici=
al.
The latter explicitly depends on speed which is a relative variable, =
determined, by definition, with respect to a certain reference frame.=
The former (according to its thermodynamic definition dS =3D dQ/T) i=
s determined with respect to the rest frame of the system in question=
, and contains no other relative characteristics. In this respect, I =
would rather compare it with the rest energy of a system, which is, b=
y definition, its absolute (observer-independent, although variable) =
characteristics.
As to a tiny fraction known by humans of an awesome amount of infor=
mation about a macroscopic system , - what about a container with liq=
uid helium in superfluid state arbitrary close to T =3D 0? If John kn=
ows its state, but Mary does not, what entropy should we attribute to=
the container?=20