A quantum system can have many states which are very similar as far as the observed properties of the system are concerned; when this happens, we can expect the system to be in a maximally random superposition of the system's allowed states consistent with its observed properties. Such degeneracy among possible states is particularly common when the system is made up of a large number of identical sub-systems.
It is usual for one of a system's observable properties to be energy; and it
is usual for the system's state with lowest energy to be quite isolated - there
will be little or no degeneracy in this ground state
. While an
isolated
system will generally change in such manner as will reduce its
energy, hence cause it to decay towards its ground state, to do so it must shed
the surplus in one manner or another - if it can do that, it's not truly
isolated
, but our standard meaning of isolated
only addresses
impact from outside as opposed to impact on its surroundings;
the universe is leaving the system alone, but the system is not obliged to leave
the universe alone. However, in the real world, just as the system tends to
lose energy to its surroundings, it surroundings will be tending to lose energy
to theirs - of which the system is a part. Thus the system will settle
on an equilibrium in which it is shedding energy (by decaying into lower-energy
states) as fast as it is being inundated with energy. This need not be the
system's ground state; and the more surplus energy the system has, typically,
the more states available to it with (at least approximately) that energy.
Thus, in practice, real material systems generally have observed properties which leave ample ambiguity as to their state, hence ample scope for random superposition of possible states. When two such systems are in a position to exchange energy, determining which will shed more to the other than it gets back depends on understanding their respective states and the effect, on each, of gaining and losing energy. The study of this issue is known as thermodynamics.
In so far as the internal states of molecules support a meaningful
temperature, one may study how they exchange
energy – both internal and gross (external) kinetic – in collisions:
this we may understand as micro-thermodynamics. On the larger scale, we can
consider how bodies, each comprising many molecules, exchange energy when they
interact: this macro-thermodynamics
is what is usually meant by
thermodynamics.
The first law of thermodynamics says heat is (a form of) energy (also known as work or mass). This is a standard observable of quantum systems; and the formalism for handling quantum superpositions of highly degenerate systems is all predicated on the observables of the sysem; so let's see what rôle heat gets to take in the solution.
Written by Eddy.