Complexity economics rejects many aspects of traditional economic theory. The mathematical models used by traditional economics were formulated in an analogy with early models of thermodynamics. These mathematical models of economics were substantially based on the first law of thermodynamics, equilibrium.[1] Later, the second law of thermodynamics, concerning the growing amount of entropy in any spontaneous physical process, was formulated by Rudolf Clausius. Proponents of complexity economics claim that traditional economic models never adapted to the latter discovery and thus remain incomplete models of reality, and that mainstream economists are yet to introduce information entropy to their models. Information entropy was developed in 1949 by C. Shannon and W. Weaver, based on Boltzmann's statistical thermodynamics, as "information uncertainty", associated with any probability distribution. Entropy has been used at least since 1988 to formulate the important concepts of organization and disorder, viewed as basic state parameters, in describing/simulating the evolution of complex systems (including economic systems).
In the light of the new concepts introduced, economic systems shall no more be considered as "naturally" inclined to achieve equilibrium states. On the contrary, economic systems - like most complex and self-organized systems - are intrinsically evolutionary systems, which tend to develop, prevailingly toward levels of higher internal organization; though the possibility of involution processes - or even of catastrophic events - remains immanent. Traditional economic models have been constructed by allowing only a very small amount of degrees of freedom, in order to simplify models. For example, the relation of unemployment and inflation is traditionally considered to be a simple function with one degree of freedom, allowing for very little entropy.
As to the practicability of theoretical instruments, there is also a crucial difference to allow for: traditional economics was conceived before computers had been invented. Computational simulations have made it possible to demonstrate macro-level rules using only micro-level behaviors without assuming idealized market actors. For example, Pareto's law can be demonstrated to arise spontaneously.
Complexity economics is built on foundations which draw inspiration from areas such as behavioral economics, institutional economics, Austrian economics, and evolutionary economics. Complexity incorporates components from each of these areas of economic thought, though the complex perspective includes many more characteristics to describe a dynamic system such as emergence, sensitive dependence on initial conditions, red queen behavior, and complex systems usually incorporate a selection mechanism as described by most general evolutionary models. There is no widely accepted specific definition for complexity as it pertains to economic systems. This is largely due to the fact that the field as a whole is still under construction.
