Synergetics, slaving principle and separation of timescales

Sherrington (1906) used the word 'synergetic' in a different sense, for a functionally co-operative collection of fibres. He argued against that view for the spinal motor root.¹ His example was the ninth subthoracic root of the monkey, which can carry fibres to the urinary bladder and to the muscles of the leg.¹ Sherrington reports that reflexes on the leg were easy to obtain through the afferent root, and reflexes on the bladder were relatively difficult.¹ His usage concerns the spatial grouping of fibres, not order parameters or timescales. The modern sense of the term is credited by later authors to Haken.²

Friston and Ao (2012) trace the order parameter concept to the study of phase transitions. They say it was generalised into the slaving principle, in which the fast, stable dynamics of dissipating patterns are set by the slow, unstable dynamics of a few macroscopic states.³ They hold that this enslaving reduces degrees of freedom and gives rise to macroscopic order.³ Kiebel, Daunizeau and Friston (2008) describe the same principle. They report that it has been applied to bimanual coordination. They say Jirsa and Haken elaborated the theory to relate it to electromagnetic observations of brain activity. They credit a separate cited work with using the framework to analyse brain dynamics measured with magnetoencephalography.²

Friston and Ao describe biological agents as generally far from thermodynamic equilibrium, even though the density over their macroscopic states is stationary.⁴ Palacios and colleagues (2020) place the slaving principle in open systems far from equilibrium. In their account, macroscopic patterns enslave microscopic ones and are also constituted by them, which they call circular causality.⁹ Schreier, Soen and Brenner (2017) varied the exploration speed D in random networks. Convergence stayed between 0.2 and 0.7 over more than five orders of magnitude of D, then fell once separation of timescales stopped holding.⁵

Kirchhoff and colleagues (2018) define an order parameter as a macroscopic feature that captures the dependencies among a system's parts.⁶ Constant and colleagues (2018) link the slow, unstable modes to phenotypic traits, as distinct from quickly fluctuating phenotypic states.⁷ Ramstead and colleagues (2019) call mixtures of Markov blanket states formally identical to order parameters, which reflect the amplitude of slow, unstable eigenmodes.⁸ Constant and colleagues call the trait mapping tempting, not established.⁷