Nonequilibrium Thermodynamic State Variables of Human Self-Paced Rhythmic Motions: Canonical-Dissipative Approach, Augmented Langevin Equation, and Entropy Maximization

Nonequilibrium thermodynamic state variables are derived for a stochastic limit-cycle oscillator model that has been used in motor control research to describe human rhythmic limb movements. The nonequilibrium thermodynamic state variables are regarded as counterparts to the thermodynamic state variables entropy, internal energy, and free energy of equilibrium systems. The derivation of the state variables is based on maximum entropy distributions of the Hamiltonian energy of the stochastic limit-cycle oscillators. The limit-cycle oscillator model belongs to the class of canonical-dissipative systems, on the one hand, and, on the other hand, can be cast into the form of an augmented Langevin equation. Both concepts are known as physical models for open systems. Experimental data from paced and self-paced pendulum swinging experiments are presented and estimates for the nonequilibrium thermodynamic state variables are given. Entropy and internal energy increased with increasing oscillation frequency both for the paced and self-paced conditions. Interestingly, the nonequilibrium free energy decayed when oscillation frequency was increased, which is akin to the decay of the Landau free energy when the control parameter is scaled further away from its critical value.