Variation Principles of Non-Linear Irreversible Processes and Negative Differential Resistivity

Two types of variation principles of linear irreversible processes established respectively by Onsager and Prigogine are generalized, so as to be applicable to non-linear processes as well. In the application to the conductor with negative differential resistivity, it is shown that Onsager's principle is suitable to the current-controlled case and Prigogine's principle to the voltage-controlled case. The spatial splittings in the conductor into high and low current filaments and voltage domains respectively occur as similarly as shown previously by Ridley, where his unreasonable conclusion based upon the minimum entropy production valid only for linear processes is revised. Finally, Onsager's and Prigogine's variation principles are approached from a unified view-point of ther modynamical theory of stochastic processes.