Investigations Of Coupling Effects In Nonlinear Thermodynamic Systems

In general,non-equilibrium thermodynamics can be divided into linear non-equilibrium thermodynamics which is close to the equilibrium state and nonlinear non-equilibrium thermodynamics which is far from the equilibrium state.It is well known that the dissipative structure can only possibly turn out when the non-equilibrium system is far away from the equilibrium state.In this paper,the stability of the non-equilibrium steady state in an ideal system with two kinds of irreversible processes has been discussed.When the system is in the nonlinear region far away from the equilibrium state,the coefficients of generalized thermodynamic forces describe the coupling relationship between flows and forces.According to the source of coupling,these coupling effects can be further divided into single coupling and complex coupling.After a detailed investigation on the excess entropy of the system,it is found that if the complex coupling effect is very weak,it is very hard for the non-equilibrium steady state to lose its stability,and a dissipative structure is almost impossible to present.However,if the complex coupling effect is strong,the steady state may lose its stability,and the dissipative structure may appear.Therefore,the complex coupling effect plays a very important role in the instability of non-equilibrium steady state,and the condition for the appearance of dissipative structure can be further described as: a dissipative structure is only possible when the system with strong complex coupling is far away from the equilibrium state.Then two ideal and open chemical reaction systems containing three components have been studied just to verify our conclusions.Firstly,two cases with no or large complex coupling in a chemical triangle reaction system had been studied,respectively,and the results show that,in the case of no complex coupling,the steady state of the system is asymptotically stable;while,in the case of large complex coupling,the steady state turns to be marginally stable.Secondly,two chemical reaction systems without or with feedbacks had also been studied,respectively.It is noted that the former and later correspond with weak or strong complex coupling,respectively,and the results show that,corresponding to the former,the steady state is stable,but the stability of the later will be possibly stable or unstable.Obviously,these results about the stability of steady state are consistent with above conclusions.