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LIT-1851: Nonequilibrium phase transitions in coordinated biological motion: critical fluctuations

2 min read

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StatusActive — read 2026-10-30 (NOTE-1433) in full, from an offprint scan posted on Kelso's lab page at Florida Atlantic University (https://ccs.fau.edu/hbblab/pdfs/Kelso_1986_PhysLettersA.pdf), read from the page images; worth reading as the first quantified report of critical fluctuations in human coordination: the standard deviation of relative phase rises before the anti-phase to in-phase switch and peaks in it, in wrist and finger experiments, with no such rise when the same movement starts in-phase. Read it knowing that its figures average a few subjects or show one representative subject, that it gives no statistical test, and that critical slowing and hysteresis are not measured in it.
Tagscomplex-systems, behavioral-integration, natural-sciences, embodied-cognition
ExtendsLIT-588 — A theoretical model of phase transitions in human hand movements
Cited as “paper” byNOTE-1433 — Kelso, Scholz & Schöner — Critical fluctuations
Cited as “source” byTHEORY-069 — Rhythmic bimanual coordination switches from anti-phase to in-phase through a nonequilibrium phase transition in relative phase, captured by the HKB equation, with critical fluctuations and critical slowing as early warning, THEORY-1227 — Haken, Kelso and Bunz model the switch of rhythmic bimanual coordination from anti-phase to in-phase at a critical frequency as the loss of one stable state of an order parameter, relative phase, derived from two coupled oscillators; Kelso, Scholz and Schöner report the variability of relative phase rising before the switch in the anti-phase pattern only, in a few subjects and with no statistical test

Graph View

J. A. S. Kelso, J. P. Scholz and G. Schöner (1986), Physics Letters A 118(6):279–284. doi:10.1016/0375-9601(86)90359-2.

Read in full on 2026-10-30 (NOTE-1433), from an offprint scan on Kelso’s lab page.

Key takeaways

  • Fluctuations rise before the switch. In the wrist experiments the SD of the point estimate of relative phase was low and steady for three four-cycle segments, rose at the segment before the transition, peaked in it, and fell once in-phase was reached (Fig. 2, averaged over 30 runs on four subjects). The finger experiments, with relative phase estimated every 5 ms and frequency raised in 0.25 Hz steps, showed the same, more clearly (Fig. 4, ten runs of one representative subject).
  • The asymmetry. Starting in-phase, neither a shift in mean phase nor a growth in fluctuation occurred as frequency rose. Below the transition, in-phase was less variable than anti-phase at every frequency (p. 283).
  • Not shown here. Critical slowing down is predicted and backed only by “very preliminary evidence” of line narrowing in the power spectrum (ref. 13); direct measures of relaxation time by perturbation were left to new experiments (p. 283). Hysteresis is not tested.

Standing in the record

Filed on 2026-10-30 at the owner’s request, with HKB 1985 (LIT-588) and Kelso, Scholz and Schöner 1988 (LIT-1873), as first-hand data for THEORY-069. The authors include the model’s own author; no independent replication is read. No instruction for machine-learning practice.

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