Hamiltonian Thermodynamics as a Unifying Theory of Dynamical and Phenomenological Methods

Dear Colleagues,

In the last two decades, classical thermodynamics, thanks to a few enlightening publications, have been elevated from phenomenological formulations to the robust formalism of Hamiltonian theory. Thus, the theory of heat has been brought to the same level of description as analytical mechanics. Particularly, thermodynamic and mechanical systems can merge in a single generally nonlinear dynamical theory to describe equilibrium and non-equilibrium processes by constructing homogeneous Hamiltonian functions of the first degree in momenta on an extended thermodynamic phase space and in a variety of representations. 

This is an important area of research if one considers that after more than a century of evolution of Hamiltonian theory, a modern geometrical (differential) description has been obtained, and important theorems and techniques for locating time invariant structures in phase space, i.e., constants of motion, have been found. Chemical reactions and spectroscopy have tremendously benefited from the application of these methods and the general investigation of the properties of highly excited molecules. 

Identifying transition states in chemical reactions as hyperbolic invariant manifolds in the molecular phase space has given an impetus in understanding chemical reactivity. The mathematical abstraction and generalization of geometric Hamiltonian theory in phase space lead to a common computational framework for working in both the microscopic and macroscopic world. 

In the field of modeling multi-physics systems, a Hamiltonian theory named port-Hamiltonian systems theory has been developed with applications in mechanical, chemical, electromagnetic, hydraulic, and control domains. It is also worth mentioning the advances in quantum thermodynamics for modeling quantum mechanical systems–bath systems consistent with the principles of thermodynamics. 

The purpose of this Special Issue is to collect original papers and comprehensive reviews which will unveil the common theoretical foundations, especially the symmetries, of all the abovementioned fields—dynamical and thermodynamical. 

This Special Issue will accept unpublished original papers and comprehensive reviews focused (but not restricted) on the following research areas: 

• Entropy;
• Contact and symplectic geometries of thermodynamics;
• Symmetries in thermodynamics;
• Reaction dynamics in phase space;
• Chemical kinetics;
• Port Hamiltonian systems for multi-physics models;
• System/bath thermodynamics (classical and quantum).

Dr. Stavros C. Farantos
Prof. Dr. Stephen Wiggins
Guest Editors

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• entropy
• Hamiltonian thermodynamics
• system–bath thermodynamics (classical and quantum)
• nonlinear dynamics
• chemical dynamics
• chemical kinetics
• port-Hamiltonian systems