In this paper, we extend Gibbs’s approach for quasi-equilibrium thermodynamic processes, and show that, in general non-equilibrium thermodynamic processes, the microscopic expression of entropy is given as S(t)=−∫dxρ(x,t)ln∫dx′ρ(x′,t)ϕΔt(x,x′,t), where ρ(x,t) is the ensemble...