An Emergent Nonlinear Thermodynamic Energy-Flow Model for Collections of Coupled Oscillators

This paper investigates the emergence of thermodynamic energy flow for collections of coupled oscillators. Unlike previous work based on averaging over stochastic forcing, a stochastic model ensemble, or time, thermodynamic energy flow is viewed as a deterministic physical phenomenon arising solely due to dimension and thus consistent with the physically observed laws of thermodynamics. For two collections of undamped coupled oscillators, the kinetic and potential energy of the respective subsystems is shown to exhibit pointwise-in-time thermodynamic energy flow before energy reversal begins. However, the rate of energy flow is found to be inconsistent with the classical exponential profile corresponding to Newton's law of cooling, whose dynamics are linear. Instead, the rate of energy flow is shown to be captured by a thermodynamic energy-flow model with quadratically nonlinear dynamics.