Stavros C Farantos

Non-Linear Hamiltonian Classical Thermodynamics and Chemical Kinetics

Thermodynamics is the theory of heat and since its first invention, it has been developed in a different fashion than other physical theories which are usually theorized by differential equations. However, at the dawn of the twenty-first century, Balian and Valentin (Eur. Phys. J. B, 21, 269 (2001)) pioneered by formulating reversible and irreversible thermodynamic processes with a Hamiltonian theory in an extended even-dimensional phase space. Hamiltonian versions of all main physical theories exist. Here, we demonstrate that non-linear molecular dynamics and thermodynamics of equilibrium and non-equilibrium processes can merge in a single dynamical theory by constructing a homogeneous of first degree in momenta Hamiltonian function on the extended thermodynamic state space and in the entropy representation. Then the way, how the system approaches equilibrium states and the entropy production during specific processes are studied. A Riemannian metric on the equilibrium state manifold (Lagrangian submanifold) is defined and that allows one to estimate the distance of the initial state from the equilibrium one. Even more interestingly, if we consider dynamical systems the kinetic equations of chemical reaction networks in accordance with Mass Action Law, with the Massieu - Gibbs thermodynamic potential as generating function of the Hamiltonian, then nonlinear properties, such as bifurcations, can be located and studied. Furthermore, the calculation of entropy production and metric provide a method to investigate the efficiency of alternative chemical reaction schemes. Numerical results are presented from the study of consecutive first order elementary reactions and the non-linear kinetic equations of autocatalytic spontaneous symmetry breaking chiral reactions.

[1] J Math Chem, 2020, DOI http://link.springer.com/article/10.1007/s10910-020-01128-z