title: Non-equilibrium thermodynamical description of rhythmic motion patterns of active systems: a canonical-dissipative approach.
abstract: We derive explicit expressions for the non-equilibrium thermodynamical variables of a canonical-dissipative limit cycle oscillator describing rhythmic motion patterns of active systems. These variables are statistical entropy, non-equilibrium internal energy, and non-equilibrium free energy. In particular, the expression for the non-equilibrium free energy is derived as a function of a suitable control parameter. The control parameter determines the Hopf bifurcation point of the deterministic active system and describes the effective pumping of the oscillator. In analogy to the equilibrium free energy of the Landau theory, it is shown that the non-equilibrium free energy decays as a function of the control parameter. In doing so, a similarity between certain equilibrium and non-equilibrium phase transitions is pointed out. Data from an experiment on human rhythmic movements is presented. Estimates for pumping intensity as well as the thermodynamical variables are reported. It is shown that in the experiment the non-equilibrium free energy decayed when pumping intensity was increased, which is consistent with the theory. Moreover, pumping intensities close to zero could be observed at relatively slow intended rhythmic movements. In view of the Hopf bifurcation underlying the limit cycle oscillator model, this observation suggests that the intended limit cycle movements were actually more similar to trajectories of a randomly perturbed stable focus.
authors.affiliation: EuroMov, Universite Montpellier-1, 700 av du Pic Saint-Loup, 34090 Montpellier, France; Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269, USA.
authors.forename: D G
authors.initials: DG
authors.lastname: Dotov
authors.affiliation: Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269, USA.
authors.forename: S
authors.initials: S
authors.lastname: Kim
authors.affiliation: Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269, USA. Electronic address: till.frank@uconn.edu.
authors.forename: T D
authors.initials: TD
authors.lastname: Frank
mesh_terms: D001696:Biomechanical Phenomena; D019277:Entropy; D006801:Humans; D008954:Models, Biological; D009068:Movement / Q000502:physiology*; D010507:Periodicity; D013816:Thermodynamics
keywords: Active Brownian motion; Canonical-dissipative systems; Human body movements; Non-equilibrium stochastic processes