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The long-term issue of entropy production in transport phenomena is solvedby separating the symmetry of the non-equilibrium density matrix ρ(t)inthe von Neumann equation,as ρ(t)=ρs(t)+ρa(t) with the symmetricpart ρs(t)and antisymmetric part ρa(t).The irreversible entropy production.(dS/dt)irr is given in M.Suzuki,Physica A 390(2011)1904 by(dS/dt)irr=Tr((H)(dρs(t)/dt))/T for the Hamiltonian (H) of the relevant system.