Theoretical physics of complex systems

Complex systems are the systems with so diverse mechanisms regulating their behaviour, that the collective (macroscopic) behaviour and properties of the whole complex are not directly determined by the microscopic (local) properties and the interactions of the constituents.

  1. Phenomenology becomes complex, highly non-linear and intrinsically collective.
  2. Often, this makes the task to formulate the problem in terms of a single scientific domain impossible. The problem needs to be addressed within a interdisciplinary framework.

Models of complex systems are governed by the equations that derive from different fields:

  • statistical physics of disordered systems,
  • information theory,
  • non-linear dynamics.

Such equations describe organized but unpredictable behaviors of fundamentally complex systems. Some of the typical theoretical features of their behavior include broken replica symmetry or ergodicity breaking.


  • Statistical inference, constraint optimization problems, coding and information theory, neural networks, machine learning;
  • Computational neuroscience;
  • Statistical physics of disordered systems, statistical mechanics of optimization problems;
  • Complex adaptive systems (immunology, economy, sustainable development, bioinformatics).