New Special Issue "Non-Hamiltonian Dynamics, Open Systems and Entropy"

Dear Colleagues,

In Hamiltonian systems, the dynamics, expressed in terms of Poisson brackets, results in a purely algebraic construction, a matter of differential geometry and topology. Algebrization of dynamics is also the simplest path to quantization, as stated by Dirac’s isomorphism, mapping the classical Poisson bracket algebra of Hamiltonian systems into the algebra of commutation brackets of quantum observables.

Classical systems with dissipation and open quantum systems are non-Hamiltonian systems, and the problem of their algebrization is currently under the spotlight. Classical systems in which dissipation coexists with a Hamiltonian structure are algebrized as metriplectic systems, or in the equivalent scheme named GENERIC, more focused on tensor operators. Open quantum systems are described with the celebrated Lindblad equations, showing striking analogies with the classical metriplectic formalism.

An excellent point about non-Hamiltonian dynamics is the role apparently played by entropy-like quantities: in classical metriplectic systems, the entropy of the medium draining mechanical energy via dissipation generates the irreversible part of dynamics. In quantum open systems, entanglement plays the role of coupling the system with the environment, giving rise to its classical properties, in a suitable macroscopic limit.

In this Special Issue, contributions will be collected on the unifying role of entropy-like quantities in algebrized dynamics of non-Hamiltonian systems, both classical and quantum. In particular, the objective is that of investigating the general relationship between irreversibility and classical behaviour, and the appearance of information-like quantities in the dynamics.

Dr. Massimo Materassi

Dr. Giuseppe Consolini

Guest Editor

https://www.mdpi.com/journal/entropy/special_issues/Hamiltonian_Dynamics