When modelling the aggregate behavior of a population over long periods of time the standard approach is to consider the system as always being in equilibrium -using averaging procedures based upon assumptions of rationality, utility-maximization and a high degree of independence amongst the agents. These analytically tractable models are fully determined by a small number of variables and the future evolution of the system is decoupled from its past. Previous studies [Akerlof and Yellen 1985, Scharfstein andStein 1990] suggested that allowing a subset of the agents to be nonmaximizing might shift the equilibrium solution but a shortcoming in those analyses prevented the possibility of non-equilibrium solutions.We show how equilibrium assumptions and solutions can be 'stresstested' by embedding the models within frameworks capable of far-fromequilibrium dynamics. This procedure is applied to Brownian motion (Random walk) asset pricing which serves as our prototypical equilibrium model.The introduction of a simple, yet plausible, form of non-maximizing coupling between the agents results in endogenous fluctuations that destabilize the equilibrium solution. These fluctuations typically consist of long periods of increasingly severe mispricing followed by rapid, unannounced, corrections. Importantly, this occurs at realistic parameter values and is consistent with the observed price dynamics of real markets. Furthermore the mispricing phase may be mistaken for a trend in the fundamentals of the equilibrium model. We argue that the 'boom-bust' nature of the destabilizing endogenous dynamics is likely to be prevalent in economic systems at all scales. All the mainstream schools of economic thought and, in turn, modern finance have been strongly motivated by the mathematical elegance and predictive success of Newtonian mechanics and statistical physics. This has resulted in mathematical models constructed so that the solution is a stable, usually unique, equilibrium described by a small number of variables and whose future evolution is independent of its past states. Indeed the notion of equilibrium has become a unifying concept in modern economics although its precise meaning varies with context. Here we shall consider those equilibrium models that attempt to describe systems involving large numbers of interacting agents over significant periods of time. Some examples, discussed briefly below, include the supply-demand curves of microeconomics, the Brownian motion description of asset prices, and the DSGE models used in macroeconomics and central banking.In the physical sciences, equilibria are most often studied as the limiting values of dynamical systems where the short-term transient behavior may not even be of interest. However, economic systems have no such end-state [Robinson 1974] and so the only remaining (legitimate) justification for equilibrium models requires the assumption that equilibrating processes operate (and dominate) over timescales shorter than or comparable to any exogenous changes. Th...