Study on the Entropy Production of a Nonequilibrium Open System

The objective of the paper is to study a nonequilibrium open system, especially its entropy production, in the framework of time-dependent projection operator. The environment of the open system may linearly deviate from its initial state under the reaction from the open system. The relevant statistical operator of the system is set as a generalized canonical one. The transport equation, entropy production and the second kind of fluctuation-dissipation theorem of the open system are derived. The memory function, influence function in the transport equation as well as the entropy production rate are expressed in terms of correlation functions of fluctuations of random force and interaction random force of the open system.