The global stability theory of a heat thermal engine model

In recent years, within the context of Finite-Time Thermodynamics, diverse studies of local stability of thermal heat engines have been proposed [1-3]. In those studies, the theory of local stability have focused on determining the relaxation times of the decaying rate to the stationary fixed points, assuming local perturbations around these values. In this work, we present a study of the global stability analysis of a thermal heat engine working at different regimes of performance. We applied the Lyapunov stability theory to construct the Lyapunov functions to prove the asymptotically stable behavior about the steady-state of intermediate temperatures in the engine model. Besides, we perform numerical integrations for the maximum power regime to corroborate the findings of the global analysis. Our study consider a linear heat transfer law and three regimes of performance: Maximum power output, maximum efficient power [4] and maximum ecological function [5].