Special Issue "Hamiltonian and Overdamped Complex Systems, Symmetry of Phase-Space Occupancy"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics and Symmetry/Asymmetry".

Deadline for manuscript submissions: 15 December 2022 | Viewed by 1983

Special Issue Editors

Prof. Antonio Rodríguez
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Guest Editor
Departamento de Matemática Aplicada a la Ingeniería Aeroespacial, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros s/n, 28040 Madrid, Spain
Prof. Dr. Alessandro Pluchino
E-Mail Website
Guest Editor
Dipartimento di Fisica e Astronomia dell'Università di Catania e INFN Sezione di Catania, Via S. Sofia, 64, 95123 Catania CT, Italy
Interests: complex systems; statistical mechanics; complex networks; agent-based models
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ugur Tirnakli
E-Mail Website
Guest Editor
Department of Physics, Faculty of Science, Ege University, 35100 Izmir, Turkey
Interests: statistical mechanics; nonlinear dynamics; complex systems

Special Issue Information

Dear Colleagues,

Complexity naturally arises in nonlinear physics and elsewhere, for instance through processes of successive bifurcations generating complex spatiotemporal patterns, or in nontrivial configurations of the phase space of chaotic Hamiltonian systems possibly involving long-range interactions, where one typically can find a mixture of chaotic seas and regions with regular motion that can lead to statistical distributions with power-law and scale-free tails.

The same can occur in systems such as complex plasmas, superconductors or colloidal systems, which can be described by dissipative approaches including repulsive particles whose equation of motion, in the overdamped limit, takes the form of a first-order differential equations, where the velocity of the particles is proportional to the force over them. Additionally, in this case, for various kinds of repulsive potentials, anomalous distributions of the local density and of the velocities can be found, both analytically and numerically.

The phase space of strongly chaotic Hamiltonian systems presents translational symmetry, as expected within Boltzmann-Gibbs statistical mechanics, consistently exhibiting the celebrated exponential distribution of energies and the Maxwellian distribution of momenta. In contrast, alternative, anomalous, distributions arise whenever this basic symmetry is broken. Such is frequently the case when weak chaos is present, for instance if long-range interactions are involved, or when memory effects play an important role, overdamped complex systems constituting a paradigmatic example of this situation. The study of the symmetry of the phase-space occupancy is thus one of the crucial features to characterize the thermostatistical properties of many complex systems. 

The aim of this Special Issue is to stimulate further investigations along these directions, particularly in connection with frameworks such as q-generalized statistical mechanics, superstatistics, stochastic thermodynamics, and other modern statistical mechanical approaches, in both classical and quantum systems where nonlocal correlations are relevant.

We are soliciting contributions (both research and review articles) covering a broad range of topics related to complexity and symmetries in space and/or time, at micro-, meso-, and macroscopic scales, possibly revealing either grounding aspects or their applications.


Prof. Antonio Rodríguez
Prof. Dr. Alessandro Pluchino
Prof. Dr. Ugur Tirnakli
Guest Editors

Manuscript Submission Information

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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. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

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Published Papers (3 papers)

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Research

Article
Exact Time-Dependent Solutions and Information Geometry of a Rocking Ratchet
Symmetry 2022, 14(2), 314; https://doi.org/10.3390/sym14020314 - 03 Feb 2022
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Abstract
The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and [...] Read more.
The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and sawtooth waves) with period T and amplitude A, we investigate the performance (energetics, mean current, Stokes efficiency) of a rocking ratchet in light of thermodynamic quantities (entropy production) and the path-dependent information geometric measures. For each G(t), we calculate exact time-dependent probability density functions under different conditions by varying T, A and the strength of the stochastic noise D in an unprecedentedly wide range. Overall similar behaviours are found for different cases of G(t). In particular, in all cases, the current, Stokes efficiency and the information rate normalised by A and D exhibit one or multiple local maxima and minima as A increases. However, the dependence of the current and Stokes efficiency on A can be quite different, while the behaviour of the information rate normalised by A and D tends to resemble that of the Stokes efficiency. In comparison, the irreversibility measured by a normalised entropy production is independent of A. The results indicate the utility of the information geometry as a proxy of a motor efficiency. Full article
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Article
Nonlinear Fokker-Planck Equation for an Overdamped System with Drag Depending on Direction
Symmetry 2021, 13(9), 1621; https://doi.org/10.3390/sym13091621 - 03 Sep 2021
Viewed by 539
Abstract
We investigate a one-dimensional, many-body system consisting of particles interacting via repulsive, short-range forces, and moving in an overdamped regime under the effect of a drag force that depends on direction. That is, particles moving to the right do not experience the same [...] Read more.
We investigate a one-dimensional, many-body system consisting of particles interacting via repulsive, short-range forces, and moving in an overdamped regime under the effect of a drag force that depends on direction. That is, particles moving to the right do not experience the same drag as those moving to the left. The dynamics of the system, effectively described by a non-linear, Fokker–Planck equation, exhibits peculiar features related to the way in which the drag force depends on velocity. The evolution equation satisfies an H-theorem involving the Sq nonadditive entropy, and admits particular, exact, time-dependent solutions closely related, but not identical, to the q-Gaussian densities. The departure from the canonical, q-Gaussian shape is related to the fact that in one spatial dimension, in contrast to what occurs in two or more spatial dimensions, the drag’s dependence on direction entails that its dependence on velocity is necessarily (and severely) non-linear. The results reported here provide further evidence of the deep connections between overdamped, many-body systems, non-linear Fokker–Planck equations, and the Sq-thermostatistics. Full article
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Article
The Superconducting Critical Temperature
Symmetry 2021, 13(5), 911; https://doi.org/10.3390/sym13050911 - 20 May 2021
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Abstract
Two principles govern the critical temperature for superconducting transitions: (1) intrinsic strength of the pair coupling and (2) the effect of the many-body environments on the efficiency of that coupling. Most discussions take into account only the former, but we argue that the [...] Read more.
Two principles govern the critical temperature for superconducting transitions: (1) intrinsic strength of the pair coupling and (2) the effect of the many-body environments on the efficiency of that coupling. Most discussions take into account only the former, but we argue that the properties of unconventional superconductors are governed more often by the latter, through dynamical symmetry relating to normal and superconducting states. Differentiating these effects is essential to charting a path to the highest-temperature superconductors. Full article
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