- Published on 06 March 2018
One of the tasks underpinning the recent development of a Statistical Mechanical theory for non-equilibrium systems concerns the understanding of the role of microscopic dynamics in giving rise to complex behaviors observed at the macroscopic level of description. A paradigmatic example is traditionally offered by turbulence, which, according to Kolmogorov’s theory, is characterized by an interplay between different physical scales in the form of an energy cascade from large to small scale eddies.
More recently, a great research activity pointed towards the understanding of the microscopic origin of a curious thermodynamic phenomenon, called “uphill diffusion”. Typically, textbooks talk about diffusion recalling that a species tends to move against the gradient of its concentration. This may no longer be the case if diffusion occurs in a multicomponent system, and the interaction among different species is responsible for the breaking of the basic tenet of the Fick’s law. More intriguing is the case of uphill diffusion taking place within a single component system in an inhomogeneous environment or in presence of a phase transition. This is a timely, and still open, research topic that recently witnessed a joint effort of theoretical and experimental work. Research in this direction spanned a broad range of models: from stochastic cellular automata equipped with Kac potentials to 2D Ising models with Kawasaki dynamics and inhomogeneous Zero Range models.
The investigation of microscopic models undergoing a stochastic dynamics proved also to be a useful tool in the investigation of the large scale behavior observed in traffic phenomena and pedestrian flows. Much of the research effort in this field regarded the development, from the details of the microscopic dynamics, of the so-called fundamental diagrams, expressing the relation between the particle flux and the particle density. Experimental data evidence the presence of complex behaviors in which the velocity decreases with the density, and different logistic regimes are identified. A recent modelling approach based on the study of lattice gas models subject to dynamical thresholds proved effective in recovering a wealth of experimental data. Remarkably, the presence of a dynamical threshold at the microscopic scale is still visible at the macroscopic scale, being ultimately responsible for the non-monotonic behavior of the fundamental diagram.
A crucial aspect of non-equilibrium statistical mechanics also concerns the study of hydrodynamic limit of particle systems. A recent line of investigation tackled, in particular, the derivation of macroscopic equations for inhomogeneous particle models and evidenced the onset of different macroscopic scenarios depending on the nature of the microscopic inhomogeneities.
This special issue aims at collecting original research articles on theory and experiments, as well as review reports on the recent trends of microscopic dynamics and its associated complex phenomena.
The topics include, but are not limited to:
- Microscopic entropy and microscopic complexity;
- Microscopic chaos: Chemical reactors, Plasmas, Brownian motion, chaotic transport theory etc.;
- Interacting particle systems: Monte Carlo simulations and hydrodynamic limits;
- Biological applications of nonequilibrium micrscopic dynamics;
- Stochastic processes and transport phenomena.
Call for papers:
We would like to invite the authors to submit their original research articles on microscopic dynamics in nonequilibrium processes. Detailed review articles on the topics are also welcome.
Submission deadline: 17 November 2018.
Articles should be submitted to the Editorial Office of EPJ ST https://articlestatus.edpsciences.org/is/epjst/home.php, and should be clearly identified as intended for the topical issue “Microscopic dynamics, chaos and transport in nonequilibrium processes” (use the pull down menu).
Santo Banerjee (Institute for Mathematical Research and Malaysia-Italy Centre of Excellence for Mathematical Science; University Putra Malaysia, Malaysia) and Matteo Colangeli (Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, Italy).