Hamiltonian classical thermodynamics and chemical kinetics

Abstract

Classical thermodynamics have recently been formulated as Hamiltonian systems elevating the theory of heat to the same level of description as analytical mechanics. Particularly, mechanical and thermodynamical systems can merge in a single dynamical theory to describe equilibrium and non-equilibrium processes by constructing homogeneous of first degree in momenta Hamiltonian functions on the extended thermodynamic phase space and in a variety of representations. By employing geometric Hamiltonian theory we show that classical chemical kinetics can also be put in a Hamiltonian framework with Massieu–Gibbs function as the generating Hamiltonian at constant temperature and pressure. A metric in the physical state manifold as well as the entropy production in irreversible chemical reactions are defined. This way we establish a common computational platform for chemical kinetics and chemical dynamics. Numerical results are presented from the study of consecutive first-order elementary reactions and the non-linear kinetic equations of a model for autocatalytic symmetry breaking chiral reactions. For the latter example, we have examined two cases; that of a closed system with fixed initial concentrations and the steady-state case.