This paper proposes the implementation of a neighboring coupling network of three identical oscillators in a cavity optomechanical system using optomechanical interactions. The objective is to investigate the irreversible dynamics characteristics of nonequilibrium transient heat transport driven by different temperature gradients and optomechanical couplings, eventually converging to a nonequilibrium steady state. A theoretical framework of entropy assessment, based on the quantum phase space approach, is used to evaluate the entropy dynamics applicable to transient processes. The study explores the transition of entropy dynamics from monotonic to oscillatory behavior under symmetric temperature thermal reservoirs from the weak coupling regime into strong coupling regime, further investigating the entropy dynamics under asymmetric temperature thermal reservoirs, where the strong coupling leads to non-regular oscillatory behavior. The analytical results show that the evolution of system entropy and thermodynamic irreversible behavior are significantly affected by the internal coupling and thermal reservoir temperatures. Furthermore, the results offer a guide for accurately measuring the evolution of irreversible dynamics in nonequilibrium transient processes in experiments, providing new ideas for the development of thermal management devices via cavity optomechanical manipulation.