Evolution of statistical averages: an interdisciplinary proposal using the Chapman-Enskog method

TL;DR

This paper proposes a novel interdisciplinary approach applying the Chapman-Enskog method, traditionally used in physics, to approximate solutions of the Boltzmann equation in fields like economics, focusing on averages and fluctuations.

Contribution

It extends the Chapman-Enskog method to a generalized phase space using information theory, deriving equations for averages and fluctuations beyond physics.

Findings

Derived equations for averages and fluctuations up to first order in the Knudsen parameter.

Applied the generalized equations to the evolution of averages in speculative markets.

Demonstrated the potential of physics-based methods in interdisciplinary contexts.

Abstract

This work examines the idea of applying the Chapman-Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of averages and their fluctuations in a generalized phase space are established up to first order in the Knudsen parameter, which is defined as the ratio of the time between interactions (mean free time) and a characteristic macroscopic time. Although the general equations here obtained may be applied in a wide range of disciplines, in this paper only a particular case related to the evolution of averages in speculative markets is examined.