Complex systems: physics beyond physics

TL;DR

This paper reviews the concept of complex systems from a physicist's perspective, emphasizing their unique dynamics, interdisciplinary relevance, and the potential for physics-based modeling using statistical physics and multiplex networks.

Contribution

It clarifies the conceptual differences of complex systems from traditional physics systems and proposes extending statistical physics and multiplex networks to better understand their dynamics.

Findings

Complex systems exhibit rich, non-trivial behaviors across disciplines.

Quantitative modeling can be achieved through extended statistical physics.

Multiplex networks effectively capture co-evolving structures in complex systems.

Abstract

Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical world. The study of complex systems forms a new interdisciplinary research area that cuts across physics, biology, ecology, economics, sociology, and the humanities. In this paper we review the essence of complex systems from a physicist's point of view, and try to clarify what makes them conceptually different from systems that are traditionally studied in physics. Our goal is to demonstrate how the dynamics of such systems may be conceptualized in quantitative and predictive terms by extending notions from statistical physics and how they can often be captured in a framework of co-evolving multiplex network structures. We mention three areas of complex-systems science that are currently studied extensively, the science of cities, dynamics of societies, and the representation of texts as evolutionary objects. We discuss why these areas form complex systems in the above sense. We argue that there exists plenty of new land for physicists to explore and that methodical and conceptual progress is needed most.