Reciprocal relations between kinetic curves

G S Yablonsky,G B Marin,A N Gorban,V V Galvita,D Constales

doi:10.1209/0295-5075/93/20004

Abstract

We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, , the kinetic operator K is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, exp(Kt), is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the i-th pure state and measure the probability pj(t) of the j-th state (j≠i), and, similarly, measure pi(t) for the process, which starts at the j-th pure state, then the ratio of these two probabilities pj(t)/pi(t) is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error.

Highlights

According to Onsager’s work [1], the fluxes in chemical kinetics are time derivatives of the concentrations and p-1 potentials are expressed through the chemical potentials
In particular, demonstrate how it is possible to verify the reciprocal relations without the differentiation of the empiric kinetic curves and solving the inverse problems, and present the experimental results which demonstrate these relations for one reaction kinetic system
We have to formulate the reciprocal relations directly between the measurable quantities. These reciprocal relations between kinetic curves use the symmetry of the propagator in the special entropic inner product

Summary

Introduction

The connections between the detailed balancing and Onsager’s reciprocal relations were clarified in detail by N. The fluxes (near equilibrium) are linear functions of potentials and the reciprocal relations state that the coefficient matrix of these functions is symmetric. In particular, demonstrate how it is possible to verify the reciprocal relations without the differentiation of the empiric kinetic curves and solving the inverse problems, and present the experimental results which demonstrate these relations for one reaction kinetic system.

Results

Conclusion