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Next consider the
relation work ,
done by entity j on entity n via the relation force upon
an entity in moving from relation 1 to relation 2.
(3.11)
If
 is
constant, then
and
I shall call the
quantity
(3.12)
the relation system
kinetic energy.
If the relation force
is such that the relation work done around a closed orbit is zero, i.e.
(3.13)
This implies the
conservation of energy.
Another way of stating
equation 8.13 or the conservation of energy is to say that any path
between point 1 and 2 requires the same transfer of energy. Consider a
path of N segments where each segment holds all
 constant,
except one, until point 2 is reached.
By Stokes' Theorem and
equation 8.13 the condition for energy conservation can be written:
Since the curl of a
gradient always vanishes, then F must therefore be the gradient
of some scalar.
(3.14)
I shall call
 the
relation potential energy. It is important to recognize that equation
8.14 is a sufficient condition for a relation energy conservative
organization but not a necessary one.
Need to add the concept that E=T+V. An entity
has a given amount of energy. The greater the energy the more powerful
the entity is in colloquial terms, i.e. the more work it can do on
other entities which is to say the more it can change the relations of
others. However, doing work on another entity consumes energy and by
the conservation of energy of the entity doing the work must be
reduced. There fore a powerful entity is one that also has a net
positive flow of energy in. Thus there must be relations in which other
entities are supplying energy.
Does E=0 imply death or the end of the entity?
If one includes the totality of all relations, including that with one’s
physical body, then, I think the answer is yes. If one is examining
some subsystem then it implies the entity is no longer present in that
subsystem.
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(C) 2005-2014 Wayne M. Angel.
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