Curie-Prigogine principle

Equation (3.306) is a general and nonlinear relation between reaction flow and affinity. However, when the reaction is close to equilibrium, we have 

Since the condition in Eq. (3.307) is highly restrictive, the linear laws for chemical reactions are not always satisfactory. 

Example 3.15 Gibbs energy and distance from global equilibrium Discuss the effect of the distance from global equilibrium for a chemical reaction system R = P. 

For the chemical reaction considered, with the concentrations of [P] and [R], we have 

This principle as originally stated by Curie in 1908, is quantities whose tensorial characters differ by an odd number of ranks cannot interact (couple) in an isotropic medium. Consider a flow J, with tensorial rank m. The value of m is zero for a scalar, it is unity for a vector, and it is two for a dyadic. If a conjugate force A) also has a tensorial rank m, than the coefficient Ltj is a scalar, and is consistent with the isotropic character of the system. The coefficients Lij are determined by the isotropic medium they need not vanish, and hence the flow J, and the force A) can interact or couple. If a force A) has a tensorial rank different from m by an even integer k, then Ltj has a tensor at rank k. In this case, Lfj Xj is a tensor product. Since a tensor coefficient Lt] of even rank is also consistent with the isotropic character of the 

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However, A and T are scaler quantities, and because Lu is only a property of the medium, in an isotropic medium it must also be a scalar. Because there is no way to define a direction for the vector heat flow, Lu = 0 is required. There can be no coupling between vector and scalar irreversible flow processes in isotropic media.10,11 This is known as the Curie-Prigogine principle. 

According to the Curie-Prigogine principle, a scalar flow, such as the rate of reaction, cannot be coupled with a vectorial flow of a transport process in an isotropic medium where an equilibrium-dividing surface is symmetric with respect to rotations around any local normal vector. However, the symmetry properties alone are not sufficient for identifying physical coupling the actual physics considered in deriving the entropy production equation and the specific structure, such as anisotropy, are necessary. 

Equation above shows the three contributions to the rate of entropy production due to heat flow, mass flow, and the chemical reaction, respectively, and excludes the viscous and electrical effects. As the membrane is assumed to be an isotropic medium, there will be no coupling between the vectorial heat and mass flows and scalar chemical reaction, according to the Curie-Prigogine principle. Under these conditions, entropy production equation identifies the conjugate forces and flows, and linear relations for coupled heat and mass flows become... 

Coupling can take place (i) amongst vectorial forces or (ii) amongst scalar forces, but no coupling can take place between vectorial and scalar forces (Curie-Prigogine principle). 

The Curie-Prigogine principle states that in an anisotropic system, no coupling of flows and forces occurs. 

By definition, an isotropic system cannot support a vector quantity associated with it. Therefore, the vectorial flows can only be related to the vector forces. The scalar reaction rates can be functions of the scalar forces and the trace of the dyadic, but not the vector forces. According to the Curie-Prigogine principle, vector and scalar quantities interact only in an anisotropic medium. This principle has important consequences in chemical reactions and transport processes taking place in living cells. 

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