  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.
