Weakly interacting statistical systems can be perfectly described by thermodynamics – provided the number of states W in the system is large. Complex systems in contrast, characterized by long-range and strong interactions, can fundamentally change their macroscopic qualitative properties as a function of the number of states or the degrees of freedom. This leads to the extremely rich behavior of complex systems when compared to simple ones, such as gases. The need for understanding the macroscopic properties of such interacting systems on the basis of a few measurable quantities only, is reflected in the hope that a thermodynamic approach can also be established for interacting systems. In particular it is hoped that appropriate entropic forms can be found for specific systems at hand, which under the assumption of maximum ignorance, could explain sufficiently stationary macro states of these systems. In this context a series of entropies have been suggested over the past decades. So far the origin of such entropies has not been fully understood within a general framework.
Article written by Rudolf Hanel and Stefan Thurner for the Santa Fe Institute.