Cite as:

Lesse P F, 1982, "A phenomenological theory of socioeconomic systems with spatial interactions" *Environment and Planning A* **14**(7) 869 – 888

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**A phenomenological theory of socioeconomic systems with spatial interactions**

**P F Lesse**

Received 16 January 1981, in revised form 19 June 1981

**Abstract. **This paper deals with a class of models which describe spatial interactions and are based on Jaynes's principle. The variables entering these models can be partitioned in four groups: (a) probability density distributions (for example, relative traffic flows), (b) expected values (average cost of travel), (c) their duals (Lagrange multipliers, traffic impedance coefficient), and (d) operators transforming probabilities into expected values.

The paper presents several dual formulations replacing the problem of maximizing entropy in terms of the group of variables (a) by equivalent extreme problems involving groups (b) - (d). These problems form the basis of a phenomenological theory. The theory makes it possible to derive useful relationships among groups (b) and (c). There are two topics discussed: (1) practical application of the theory (with examples), (2) the relationship between socioeconomic modelling and statistical mechanics.

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