You are cordially invited to the Colloquium organized by Faculty of Science.
Speaker: Professor Henrik Jeldtoft Jensen (Professor of Mathematical Physics and leader of the Complexity Science Centre at Imperial College London, UK.)
Title: “Quantifying Emergence: tools from statistical mechanics and information theory”
Date: Wednesday, 17 September 2025
Time: 15:30
Place: UNAM SU-01
Abstract:
Complexity Science can be considered as the systematic study of emergence [1]. We take the pragmatic view point and consider emergence to be the occurrence of properties, or phenomena, at the aggregate level, which the individual parts do not possess. This viewpoint stresses that new emergent properties can only appear when components are interacting.
Statistical mechanics has developed methods to quantify and derive emergent properties from a knowledge of the interaction between components. Perhaps the most spectacular example of this consists in the equilibrium theory of order parameters describing the macroscopic change from one phase to another. We will briefly recall this in the context of how vortices in the 2dXY model can be handled as emergent particles.
Many complex systems are not in equilibrium and cannot easily be described in terms of Hamiltonians and Boltzmann probability weights. To analyse such systems one may instead need to start from data and often an abundance of data. Think for example of brain scans such as EEG and fMRI. From such data one may try to quantify emergent properties and relations by use of statistical interdependence, which is what current studies in information theory attempt to do, see e.g. [2].
We will briefly discuss the difference between the mechanistic approach of statistical mechanics and the probabilistic method of information theory. We will highlight strengths of the later but also point out that care is necessary.
References
[1] Henrik Jeldtoft Jensen, Complexity Science. The study of emergence, Cambridge Univesity Press, 2022 [2] Fernando Rosas Pedro A.M. Mediano, Michael Gastpar and Henrik J. Jensen, Quantifying high-order interdependencies via multivariate extensions of the mutual information, Phys. Rev. E. 100, 032305 (2019)