Irreversibility and entropy production in transport phenomena, II: Statistical-mechanical theory on steady states including thermal disturbance and energy supply

► The entropy production and its time derivative have been obtained in transport phenomena. ► The principle of minimum entropy production is justified microscopically. ► General expressions of nonlinear currents have been obtained in two ways. ► A mechanical formulation of thermal disturbance is presented to derive thermal conductivity. ► The heat supply is expressed using the density-matrix formalism to express a steady state.