Economics and Thermodynamics: von Neumann’s Problematic Conjecture

Abstract

Of the attempts to find analogies between thermodynamics and economies there is alas no end. But the mathematical genius John von Neumann has earned the right to command our investigation when he suggests that his growth model (1945; earlier 1932 and 1937) defines a function Value of Inputs_t/Value of Outputs_t+1

$$ = \sum\limits_i^n {\sum\limits_j^m {{P_i}} } {A_{ij}}{X_j}/\sum\limits_i^n {\sum\limits_j^m {{P_i}} } {B_{ij}}{X_j}$$

$$ = \phi \left( {P,X} \right)$$

whose “role seems to be similar to that of thermodynamic potentials in phenomenological thermodynamics.” (1945, p.1)