Abstract

A theory of temperature dynamics in many-body systems driven by time-dependent external sources is introduced. The formalism is based on the combination of perturbation theory and the fluctuational-electrodynamics approach in many-body systems. By using response theory, an explicit formula for temperature and phase shifts is derived and expressed in terms of the amplitude and phase of external power sources. Although the proposed method is highly efficient because it can skip the transient response, it is valid when external powers are weak. As an illustration of this theoretical framework, we have shown the dynamics of temperatures in one, two, and three degrees of freedom systems driven by sine wave input powers. Finally, we highlight some emergent phenomena arising from purely dynamical many-body effects, including amplification, attenuation, delaying, or accelerating temperature responses. This work could find important applications in the domain of dynamical thermal management at the nanoscale.