11. Generalized Exchange and Laws of Conservation
L. G. Kreidik (translation from Russian T. S. Kortneva and G. P. Shpenkov)
We will consider kinematic exchange between a system and the environment
on the Z-level of rest-motion (Fig. 2.15).
Fig. 2.15. A graph of Z-level exchange.
Let motion-rest be transferred from the environment to the system and the amount of motion-rest be transferred from the system to the environment along the kinetic channel and be transferred by the system over the potential. If , then
, , , (2.262)
where is a parameter of any level of motion, r is kinetic resistance or kinetic elasticity, k is potential resistance or potential elasticity, and are differentials of particular states.
In a general case, the resistances of the exchange channels depend on the state of the system, environment, and the character of the exchange channels; in the linear approximation they are constant. Their inverse values, g and C , will be called kinetic and potential conductivities, respectively.
Each of the differentials of exchange over a direct and two inverse channels determines the amount of mutual exchange equal to the difference of partial components of exchange. The rest-motion gained by the system is equal to the sum of exchanges in the three channels. Thus, we have
Hence, we arrive at the equation of exchange in the form:
The equation of exchange is simultaneously the equation of the state of the system.
We will write the exchange-state equations for -, -, - and - levels:
, , (2.265)
, , (2.267)
, . (2.268)
In a broad sense, the first terms in the left-hand sides of the equations are kinetic momenta, the second and third terms are kinetic and potential momenta of the feedback with the environment.
If we introduce the generalized charge
, , , (2.269)
where a is the characteristic length, then in terms of charges the equation for the -level becomes:
For the -level it will be represented by the equation of current:
Finally, on the -level the equation takes the form:
If the system is closed over the channel (), it is closed over all overlying channels and in a general case, it is not closed over all underlying channels
Energy description of the levels , , and is expressed by
If the system is closed over the kinetic channel, i.e. , then energies
, , (2.277)
, , (2.278)
are conserved. If the system is open, motion-rest is also conserved but within the common bounds of the system and environment.
Copyright © L.G. Kreidik , 2001-2005