Non-equilibrium thermodynamics of marginal- and conditional-open chemical systems

Abstract

Every open chemical system treated in this paper is restricted to the case involving a sequence of monomolecular reactions. Various kinds of probability distribution governing it are introduced according to the situations in which it is placed. The chemical system subject to marginal distribution is given the term marginal-open system MO. The open chemical system Ō discussed by Nicolis and Babloyantz can be regarded as the limiting system of MO. For an open chemical system, itself in contact with an external reservoir of finite volume, the probability distribution conditioned on the marginal distribution for the external reservoir in an arbitrarily fixed state is more appropriate. Such an open chemical system is called a conditional-open system CO. However, in the case of the external reservoir of infinite volume, although it is not certainly trivial, another conditional probability distribution has to be proposed; it is derived on the hypothesis that the probability distribution for an arbitrary total number of molecules in the open chemical system is known. The open chemical system so specified is called conditional-open system C O ̄ . It is shown that for each system MO, CO and C O ̄ the change of entropy starting from the steady state provides a Liapunov function under some conditions and that the steady state is asymptotically stable. The relation of the entropy change to non-equilibrium fluctuations of chemical components in each system is discussed in comparison with that in the corresponding open chemical system Ō, for which the steady state surely exists and is always stable. It is shown that the concept of C O ̄ is useful for investigating the phenomenon of steady-state coupling.