Equilibrium, Disequilibrium, Non-equilibrium

Equilibrium and non-equilibrium systems have been a recurring theme at many panels in this year’s SEA conference leading me to muse on the differences between them. Please note that non-equilibrium is not the same things as disequilibrium. The difference being that disequilibrium is a property of some systems that have (stable or unstable) equilibria, usually used to characterize the dynamics of the system when outside of equilibrium. On the other hand non-equilibrium systems are systems that do not posses equilibria.
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One common, avoidable, and completely unnecessary confusion is that the way one can tell the difference between disequilibrium and non-equilibrium is through stability analysis, of the type that can only be carried out with mathematical models. We must not confuse physics envy for analytic sophistication. This view entails confusing non-equilibrium for systems with unstable equilibria (typically by analyzing the properties of fixed points in dynamic systems, Strogatz has posted all his lectures online, Yey!). But non-equilibrium is a category that applies to systems, not a property of those systems that have equilibra, a category mistake.
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Consider the definition of economic equilibrium: the vector of prices and the vector of quantities such that all possible gains from trade have been exploited. Two things that have been extensively pointed out by others are immediately apparent, equilibrium can never describe any real economic system unless all change is considered to be exogenous to the system. It then follows that if we assume that all change is exogenous, entrepreneurship is a disequilibrium path that characterizes the response of the system after it gets jolted out of equilibrium. In an equilibrium universe entrepreneurship is the name we give to disequilibrium, which is then by definition always equilibrating. This is as formal a definition of a closed ended economics I can give imagine. An open ended economics can then be defined simply as a non-equilibrium economics, and while it may seem difficult all it entails is to recognize that economic models are not representations of reality in the same sense that physics models are. Entrepreneurship is driving the dynamics (but what of coordination? more on that to come) of the non-equilibrium system, while in equilibrium/close-ended economics, entrepreneurship is merely the name we give to disequilibrium adjustment of the system.
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