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 . (2.263)

Hence, we arrive at the equation of exchange in the form: (2.264)

or (2.264a)

or . (2.264b)

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) , (2.266)

or , , (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: . (2.270)

For the -level it will be represented by the equation of current: . (2.271)

Finally, on the -level the equation takes the form: . (2.272)

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 , (2.273) , (2.274) , (2.275) . (2.276)

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.

Theoretical Dialectical Journal: Physics-Mathematics-Logic-Philosophy, N.2, site http://www.tedial.narod.ru/