Thermodynamics of firms' growth

The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper we show that a thermodynamic model based on the Maximum Entropy Principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical framework is tested against a comprehensive data-base of Spanish firms, which covers to a very large extent Spain's economic activity with a total of 1,155,142 firms evolving along a full decade. We show that the empirical exponent of Pareto's law, a rule often observed in the rank distribution of large-size firms, is explained by the capacity of the economic system for creating/destroying firms, and can be used to measure the health of a capitalist-based economy. Indeed, our model predicts that when the exponent is larger that 1, creation of firms is favored; when it is smaller that 1, destruction of firms is favored instead; and when it equals 1 (matching Zipf's law), the system is in a full macroeconomic equilibrium, entailing "free" creation and/or destruction of firms. For medium and smaller firm-sizes, the dynamical regime changes; the whole distribution can no longer be fitted to a single simple analytic form and numerical prediction is required. Our model constitutes the basis of a full predictive framework for the economic evolution of an ensemble of firms that can be potentially used to develop simulations and test hypothetical scenarios, as economic crisis or the response to specific policy measures.