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Perhaps [conductivity] is not the essential problem.
to define the energy in an electric field, one considers a
set of charges as they are moved, isothermally, from infinity to their
places in the system.
If this assembling is infinitely slow (to avoid
friction), the work of assembly is identified with the energy of the
system.
An essential condition is that all of the forces are CONSERVATIVE
- if, for instance, two opposite charges are drawn apart at some stage,
the energy of the system must increase at the expense of the work you
spend but NOT at the expense of heat absorbed from the surroundings.
This
IS the case when you draw two opposite charges apart in a vacuum, but does
NOT seem to be the case when you draw them apart in a dielectric liquid
(e.g. water).
In the latter case, conductivity is irrelevant - the
essential factor is the increased liquid pressure between the charges that
pushes them apart.
Now the problem: is this pressure analogous to gas
pressure with respect to the fact that, as the gas expands slowly and
isothermally, it absorbs heat from the surroundings? If the analogy does
exist, I am not sure about the consequences - somehow non-conservative
forces of this type will have to be included in the general theory.