Freedom, Emergence, and Dimensions

The Freedom, Emergence, and Dimensions (FRED) project will explore contributions from the Ergodic Theory of Chaos to systems analysis.

© Andreasg | Dreamstime

© Andreasg | Dreamstime

The project will focus on linking two different views of reality: the statistical view, which treats everything as a single observation independent of others; and the dynamic view, where we look at how things are connected to each other. Here, the degrees of freedom will be defined by the number of drivers of the system.

The degrees of freedom of a dynamic system are given by the number of independent drivers. Along with the evolution of a system, properties may emerge that add more degrees of freedom. In geometry the dimension of an object is defined by its extensions along a degree of freedom. A curve is 1-dimensional, an area 2-dimensional, a body 3-dimensional, and evolution over time adds a fourth dimension. The Rényi-dimensions Dq(q=0,1,2) of dynamic systems resemble a generalization of the geometric dimensions assessing additional aspects contributing to the degrees of freedom of an object or system.

The Ergodic Theory of Chaos provides two additional measures:

  • Entropy describing the amount of information contained in a system; if a system evolving over time exhibits an increase in entropy its information content is reduced;
  • Characteristic exponents for the time evolution of a system describe the rate of deviation of initially close development trajectories, i.e. the increase of information content. They are negative for stable systems (trajectories merge onto fixed points or limit cycles, i.e. the system exhibits self-similarity and statistical system descriptions are valid). If one of the exponents is positive the system exhibits sensitive dependence, that is, becomes chaotic.

The goals for the project are to:

  • provide numerical measures of system resilience;
  • characterise the rate of information destruction/creation within a system;
  • assess time horizons of predictable system evolution; and
  • to establish links between statistical and dynamic views of reality.

The main outcomes of the project are:

  • steps forward towards a thermo-dynamic theory of ecosystems and
  • incorporating results into the G4M platform.

Future strategies include integration of the results into next generation vegetation models, with variable complexity, and application to other models in natural, economic, social sciences.

The FRED team consist of members from IIASA programs Ecosystems Services and Management and Advanced Systems Analysis Programs and institutions BOKU University, Towson University, University of Kwa Zulu Natal, and the Institute of Advanced Study.

Project partners

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Last edited: 22 September 2016


Stephan Pietsch

Guest Senior Research Scholar Exploratory Modeling of Human-natural Systems Research Group - Advancing Systems Analysis Program


1 August 2016 - 31 July 2017

International Institute for Applied Systems Analysis (IIASA)
Schlossplatz 1, A-2361 Laxenburg, Austria
Phone: (+43 2236) 807 0 Fax:(+43 2236) 71 313