Dynamics Beyond the Hamiltonian: Dissipation in Classical Metriplectic Systems and Quantum Non-Unitary Systems
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".
Deadline for manuscript submissions: 30 July 2025 | Viewed by 76
Special Issue Editor
Interests: dissipative processes; metriplectic dynamics; information theory and dynamical systems; space weather
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
The algebrization of dynamical relationships is a paramount feature of Hamiltonian systems in which evolution and its diagnostics are described through the same differential geometry tools useful to study the effects of “transformations (e.g., rotations, translations, and gauge transformations) on the phase space, namely the Poisson bracket algebra. This has a tremendous equivalent in the quantum world in terms of the commutator algebra, giving both the dynamics of observables (in the Heisenberg representation) and their transformation rules. When dissipation comes into play, this beautiful framework breaks down: the dynamics cannot be reduced to Poisson–commutator algebra, even if those mathematical tools still implement transformations on the phase space and observables.
Many classical dissipative systems may be recast into a Leibniz algebra framework, named metriplectic formalism (or its full equivalent, GENERIC tensor formalism) in which the Hamiltonian limit is well represented by a purely Hamiltonian dynamic with Poisson brackets, while the “dissipative addendum” is a semi-metric bracket, able to increase a quantity identified with the entropy of the system. In such a scheme, transformations through Poisson brackets do not increase entropy; hence, they do not make observables age, while the semi-metric bracket transforms the phase space and observables, making them age as entropy is produced.
In quantum systems, no exact parallel to the metriplectic dynamics is known, even if the full parallel between classical Poisson bracket algebra and quantum commutator algebra could be expected to be extendable to some operator algebraic structure wider than that of commutators. Recently, studies have been carried out on the relationship between the evolution of open quantum systems described, for instance, through the Lindblad equation, and classical metriplectic systems, in which classical structures go beyond the Hamiltonian regime parallel to quantum non-unitary evolutions; moreover, through the use of a system of coherent states, the bridge between quantum systems and classical ones may be easily traced in the macroscopic limit.
With this Special Issue of Entropy, we would like to collect new and updated applications and theoretical developments of the algebrization of dynamical systems that go beyond the Hamiltonian framework, with particular reference to classical metriplectic (GENERIC) formalism, quantum open system and non-unitary evolutions, and the relationship between the two. In particular, submissions are encouraged concerning, but are not limited to, the following:
- The relationship between MF and non-equilibrium thermodynamics;
- Turning known theories into metriplectic systems;
- Open and dissipative quantum systems;
- Metriplectic systems in space physics, applied physics and technology and biophysics;
- MF and GENERIC formalism;
- Non-unitary quantum dynamics and non-Hermitian Hamiltonians.
If you are interested, please send us an email with a tentative title and short abstract by August 1, 2025.
Dr. Massimo Materassi
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- metriplectic formalism
- generic formalism
- quantum open systems
- dissipation
- collisional plasmas
- trophic webs with losses
- maximum and minimum entropy production principles
- non-unitary quantum systems
- macroscopic limit of quantum systems
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.
Further information on MDPI's Special Issue policies can be found here.
