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

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