The zone-size-dependent entropy formula and spatial interaction modelling: An additional note

Abstract.

This paper consists of two basic sections. The first is a free continuation of our previous paper published elsewhere and the subject to which it returns is the extension of Wilson's entropy formula made by Senior. Recall that discussion produced there focused on two issues: specification of the term representing an extension and implications following from this extension, particularly for deriving singly constrained and unconstrained interaction models. The prime objective of the first section of this paper is to apply new insights in order to support the findings made in the previous paper. To reach this aim two approaches have been elaborated: within the first the zone-size term of an objective function is not fixed but modified according to constraints being imposed, within the second the zone-size term is fixed, indepedently of constraints. The second approach implies introducing “zone size” and “zone capacity” as two distinct concepts. The second section of the paper is devoted to additional consideration concerning extension of Wilson's entropy formula. Extension suggested by Tomlin is presented the purpose of which is no longer to account additional microstates, as it was the case in Senior's extension, but to account that not all microstates may a priori be equiprobable. Discussion is focused on the specification of the term reflecting this situation.