# ABSTRACT OF PAPER

Title: From the Ergodic Hypothesis to the Ergodic Axiom

Author: *Kirstein Mark*

The direction of the mathematisation of predominant economics is unthinkable without the tacit underlying assumption of ergodicity. Despite its foundational character, the assumption of ergodicity is either unknown or virtually unrecognised in the economic discipline, although closely intertwined with the equilibrium concept yet absent from the curriculum, as contrasted with such popular assumptions like rational expectations formation, representative agent, efficient markets, perfect competition, etc. Nevertheless, ergodicity is more fundamental than all of the mentioned popular assumptions. Ergodicity is a property of a mathematical system and originated from statistical mechanics, invoked by L. Boltzmann, who literally called it a ‘Kunstgriff’ to simplify the needed mathematics. Ergodicity is fulfilled, if the time average of a system or process equals its ensemble average. However, if the time average of a system is unequal to its ensemble average, the system or process is called nonergodic. The time average is the average of one observed trajectory or realisation of a process (one time series). The ensemble average is the average over every possible state of a system. Nonergodicity is a necessary property of a mathematical model, if the model is supposed to describe occurences of endogenous novelties and change. The nonergodic case is the more general, whereas the ergodic case is much easier to handle mathematically. Capitalistic economies are downright defined through their potential of evolution and non-routine change and so are its very centerpiece financial markets. Accepting that proper mathematical models of economic or financial processes should posses the property of nonergodicity, puts emphasis on the crucial role of time through which a certain amount of uncertainty enters into economic reasoning. This contribution seeks to clarify this specific relation between the idea of (non)ergodicity from statistical mechanics and its role in and for economics and finance. The change of status is analysed, as the ergodic hypothesis in physics became the ergodic axiom in economics. Therefore, we follow the idea from rational mechanics of J. W. Gibbs via E. B. Wilson to P. A. Samuelson and from him into rational economics. This methodological spillover from the natural sciences to economics and the assumption of ergodicity in particular is discussed. It lead to and enabled the mathematisation of economics since the 1940s. Before I conclude, the rhetoric of ergodic economics is dissected and found to be rather special, namely consisting of a near-complete concealment of the tacit assumption of ergodicity.

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