Metriplectic Formulation of Dynamical 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 36
Special Issue Editor
Interests: dissipative processes; metriplectic dynamics; information theory and dynamical systems; space weather
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Dear Colleagues,
Metriplectic systems evolve through their phase-space via an algebra of brackets (Leibniz algebra), which generalizes the Poisson algebra of Hamiltonian systems. While Hamiltonian systems have a total, conserved Hamiltonian H that generates motion through an antisymmetric Leibniz bracket satisfying the Jacobi identity, metriplectic systems add to this scheme a semidefinite symmetric bracket, referred to as a semimetric bracket, generating some additional component of dynamics through a Casimir quantity S, with zero Poisson bracket with any other quantity. The semimetric bracket of the Hamiltonian H with any quantity of the system is constructed to be zero: all in all, the metriplectic motion conserves H, while the suitable semidefinition of the semimetric bracket makes S only grow with time. Such systems may then mimic classical isolated systems with dissipation, whose total energy H is conserved, while S can be interpreted as the time-increasing entropy of the microscopic degrees of freedom towards which dissipation drives energy irreversibly.
In the metriplectic formalism (MF), dissipative entropy-producing systems may undergo the following benefit-characterizing Hamiltonian systems: conservation principles transparently obtained from symmetries; use of algebraic methods for numerical codes reproducing the dynamics; search for variational principles; and possible construction of corresponding quantum systems.
With this Special Issue of Entropy, we would like to collect new and updated applications and theoretical developments of dynamical systems described via metriplectic formalism. In particular, submissions are encouraged on the following topics (but not limited to them):
- Relationship between MF and non-equilibrium thermodynamics;
- Turning known theories into metriplectic systems;
- Relationship between MF, and open and dissipative quantum systems;
- Non-dissipative metriplectic systems;
- Metriplectic systems in space physics;
- Metriplectic systems in applied physics and technology;
- Metriplectic systems in biophysics;
- MF and GENERIC formalism.
If you are interested, please send us an email with a tentative title and short abstract by 30 July 2025. We look forward to your submissions.
Dr. Massimo Materassi
Guest Editor
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Keywords
- metriplectic formalism
- generic formalism
- quantum open systems
- dissipation
- collisional plasmas
- trophic webs with losses
- maximum and minimum entropy production principles
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