Field Theory in Practice


  • José Méndez Omaña Beuth-Hochschule für Technik Berlin, Berlin, Germany



field theory, mathematical models of human behaviour, social event entropy


The aim of this paper is to present K. Lewin’s Field Theory in practice, applying it to evacuation simulations. The construction of the field is discussed from the scratch in order to define the psychological space of a social event. Then, we illustrate the interplay of the physical and the psychological aspects of a mathematical model of human behavior presenting and discussing evacuation simulations of one event. At first we simulate the physical situation and then we calculate an evacuation time applying an elementary microscopic model. An empirical plausibility control is presented. When we apply mathematical modeling or cybernetic methods to social sciences we are said to be careful. Nevertheless, a social event might be considered, on a natural way, as a set of time series, from the point of view of statistics. In this paper we restrict ourselves to introduce probabilities of random variables associated to the physical and the psychological space and define a measure for the evacuation simulation: The entropy of the event, merging the physical and the psychological spaces.


M. Chraibi, A. Schadschneider and A. Mackens, “Quantitative Description of Pedestrian Dynamics

with a Force-Based Model”, arXiv: 0910.2343v1 [physics.soc-ph], 2009.

D. Helbing and P. Molnar , “Social Force Model for Pedestrian Dynamics,” in Physical Review E,

vol.51 (5), pp. 4282-4286, 1995.

H. Klüpfel, T. Meyer-König and M. Schreckenberger, “Models for crowd movement and egress

simulation”, in Proceedings of Traffic and Granular Flow ’03, Berlin, 2004a, pp. 357-372.

K. Lewin, Principles of Topological Psychology, New York: McGraw-Hill, 1936.

K. Lewin, Field Theory in Social Sciences, New York: Harper & Brothers, 1951.

K. Lewin, “Defining the field at a given time (1941)”, in Psychological Review 50(3), pp. 292-310,

J. Méndez Omaña, “Field Theory and Quantitative Models for Pedestrian Dynamics”, in

Transportation Research Procedia, vol. 2, pp. 442-445, 2014

W.M. Predtetschenski and A.I. Milinski, Personenströme in Gebäuden, Berechnugsmethoden für

die Projektierung, Köln-Braunsfeld: Rudolf Müller, 1971.

A. Schadschneider and A. Seyfried, “Validation of CA Models for Pedestrian Dynamics with

Fundamental Diagrams”, in Cybernetics and Systems: An International Journal, vol. 40 5, pp.


I. von Sievers, A. Templeton, F. Künzner, G. Köster, J. Drury, A. Philippides, T. Neckel and

H. Bungartz, “Modeling social identification and helping in evacuation simulation”, in Safety

Science, vol. 89, pp. 288-300, 2016.

C. E. Shannon, “A Mathematical Theory of Communication”, in The Bell System Technical

Journal, vol. 27, pp. 379-423, 623-656, 1948.

N. Wiener, Cybernetics: Or control and Communication in the Animal and the Machine, Cambridge

MA: M.I.T. Press, 1948.




How to Cite

Omaña, J. M. (2020). Field Theory in Practice. Collective Dynamics, 5, 69–76.



Proceedings of Pedestrian and Evacuation Dynamics 2018