Non-equilibrium thermodynamical description of rhythmic motion patterns of active systems: A canonical-dissipative approach

Authors

Dobromir Dotov, University of Nebraska at OmahaFollow
S. Kim, University of Connecticut
T. D. Frank, University of Connecticut

Author ORCID Identifier

Dotov https://orcid.org/0000-0002-5543-360X

Document Type

Article

Publication Date

1-22-2015

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.

Comments

This is an Accepted Manuscript of an article published by Elsevier in Biosystems on January 22, 2015, available online: https://doi.org/10.1016/j.biosystems.2015.01.002

DOI

https://doi.org/10.1016/j.biosystems.2015.01.002

Journal Title

Biosystems

Volume

128

First Page

26

Last Page

36

Recommended Citation

Dotov DG, Kim S, & Frank TD (2015). Non-equilibrium thermodynamical description of rhythmic motion patterns of active systems: a canonical-dissipative approach. BioSystems, x(xxx). doi:10.1016/j.biosystems.2015.01.002 https://doi.org/10.1016/j.biosystems.2015.01.002

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.