Where does chaos collide?

Ludwig Boltzmann's 1872 kinetic theory of gases introduced the assumption now called molecular chaos, the Stosszahlansatz: that the velocities of two molecules about to collide are statistically independent, uncorrelated before they meet. Building on this assumption, his H-theorem showed how a gas approaches equilibrium and gave a mechanical account of the second law of thermodynamics. Here chaos means the absence of correlation among vast numbers of particles, a randomness assumption at the foundation of statistical physics, which is a different idea from the primordial void of myth, from unpredictability produced by fixed deterministic rules, or from the balancing point of an organization.[1]

Unit

An independence assumption applied to the velocities of colliding molecules

Recovery means

Not applicable

Measured by

Expressed mathematically as the factorisation of the two-particle velocity distribution in the Boltzmann collision term

Edward Lorenz's 1963 Deterministic nonperiodic flow found that a simple, fully deterministic set of weather equations could produce behaviour that never repeats and that depends so delicately on the starting conditions that long-range prediction becomes impossible: a tiny change in the input leads to a completely different outcome. Li and Yorke gave this behaviour its now-standard name in their 1975 paper Period three implies chaos. Here chaos is a precise property of deterministic systems, apparent randomness with no random input at all, which is unlike a myth's opening void, unlike an assumption that particles move independently, and unlike a management regime poised between order and instability.[2][3]

Unit

A property of a deterministic dynamical system, gauged by sensitivity to initial conditions

Recovery means

Not applicable

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Detected through positive Lyapunov exponents, aperiodic bounded trajectories, and strange attractors in the state space

Christopher Langton's 1990 paper Computation at the edge of chaos named a narrow regime, sitting between rigid order and full disorder, in which complex systems can process information and adapt most effectively. Brown and Eisenhardt's 1997 study of fast-moving firms carried the idea into organization science, describing companies that succeed by holding themselves at this boundary, structured enough to be coherent yet loose enough to keep improvising. The referent is a favourable operating regime for an adaptive system, a boundary condition studied in complexity and management research, and it is a distinct idea from a cosmic beginning, from an independence assumption about gas molecules, or from the bare property of a deterministic equation.[4][5]

Unit

A regime or boundary condition of a complex adaptive system

Recovery means

Not applicable

Measured by

Described in organizations by the balance of structure and improvisation, and in models by tuning a system near an order to disorder transition