On geometry of multiscale mass action law and its fluctuations

The classical mass action law in chemical kinetics is put into the context of geometric multiscale thermodynamics, which allows for description of chemical reactions with inertial effects. The kinetics is extended to an enlarged state space with reaction rates as new state variables, and it has the structure a Lie-algebroid dual. Subsequently, the dynamics is lifted to the Liouville description within kinetic theory of the enlarged state space, so that we can include also dynamics of fluctuations. The lifted kinematics has the geometric structure of a matched pair, which allows for reduction to moments by a Lie-algebra homomorphism, as in the Grad hierarchy. In particular, the first and second moments then lead to evolution equations for chemical kinetics with inertia and for correlations between composition and reaction rates. Finally, dissipation is added in the extended state space which leads to the classical mass action law when the moments relax to their respective quasi-equilibria. We demonstrate, for instance, the possibility of oscillating homogeneous chemical reactions, and how correlations between composition and reaction rates contribute to the chemical kinetics. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The classical mass action law in chemical kinetics is integrated into the framework of geometric multiscale thermodynamics, enabling the description of chemical reactions with inertial effects. The kinetics is expanded to a larger state space with reaction rates as new state variables, exhibiting a Lie-algebroid dual structure. The dynamics is then enhanced to the Liouville description within the kinetic theory of the enlarged state space, allowing for the inclusion of fluctuations. The lifted kinematics possesses a geometric structure of a matched pair, enabling reduction to moments by a Lie-algebra homomorphism, akin to the Grad hierarchy.