The Theory of Society  by Wayne M. Angel, Ph.D.

Relation Thermodynamics: Extensive Parameters















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Perhaps the most obvious macro level parameter is the number of each type of entity of which the system is composed.  Nk will represent the of number of entities of type k in the system under consideration.

The second macroscopic parameter I wish to consider is the total internal relation energy of the system.  This is the sum of all the relation kinetic and relation potential energy of the system as defined above under relationship dynamics.  I shall call it E. 

The third macroscopic parameter I wish to consider is the relation interdependence configuration space volume.  I define it as

.

For simplicity I shall call this macroscopic parameter relation volume.  Conceptually it can be thought of as representing the size of the interdependence of the entire system.  The larger this volume the greater the average distance between entities and therefore the smaller the interdependence and, of course, vice versa.

Introduced this way this parameter and its definition may seem to be somewhat mysterious with little justification.  Indeed, I could present some qualitative reasons indicating its significance; however its value will ultimately be determined by its usefulness in a quantitative formulation.  Therefore, I will let its merit rest solely upon how it fits into that quantitative formulation. 

The macroscopic parameters E, V, Nk have a common property that will prove to be very significant.  Consider two systems characterized by EA, VA, NkA and EB, VB, NkB.  If system A and system B are now combined, then

            EC = EA + EB

            VC = VA + VB

            NkC = NkA + NkB

             Parameters that have values in a composite system equal to the sum of the values in each of the subsystems are called extensive parameters.  Extensive parameters play a key role throughout thermodynamics theory.

                                                                                                Callen [1960, 9]

 I shall find occasion to use various ratios of the extensive parameters.  In a system containing r entity types I shall call the r ratios entity fractions, and the quantity the average entity volume.

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