Energetics of open systems and chemical potential from micro-dynamics viewpoints

We present the energetic aspect of open systems which may exchange particle s with their environments. The motion of the particles is described by the classical Langevin dynamics. We study the energy balance relation among the open system and the environments along a particular realization of the sto chastic process. It is clarified how much energy each particle carries when it enters or leaves the system. This energy is definitely different from t he chemical potential. Then, the chemical potential is consistently interpr eted from the viewpoint of energetics, paying attention to the difference o f the level of description between the thermodynamics and the kinematics.