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Contents tagged “phase space”

There are 2 contents with the tag “phase space”:

  1. Comparing Symmetries in Models and Simulations

    Comparing Symmetries in Models and Simulations

    Springer Handbook of Model-Based Science

    We distinguish mathematical modeling, computer implementations of these models and purely computational approaches by their symmetries and by randomness.


    Computer simulations brought remarkable novelties to knowledge construction. In this chapter, we first distinguish between mathematical modeling, computer implementations of these models and purely computational approaches. In all three cases, different answers are provided to the questions the observer may have concerning the processes under investigation. These differences will be highlighted by looking at the different theoretical symmetries of each frame. In the latter case, the peculiarities of agent-based or object oriented languages allow to discuss the role of phase spaces in mathematical analyses of physical versus biological dynamics. Symmetry breaking and randomness are finally correlated in the various contexts where they may be observed.

    Keywords: Phase Space, Symmetry Breaking, Chaotic Dynamic, Object Oriented Programming, Genetically Modify Organism

    Longo, G., and Maël Montévil. 2018. “Comparing Symmetries in Models and Simulations.” In Springer Handbook of Model-Based Science, edited by M. Dorato, L. Magnani, and T. Bertolotti, 843–56. Springer. https://doi.org/10.1007/978-3-319-30526-4
    Manuscript Citation Publisher Full text
  2. Extended criticality, phase spaces and enablement in biology

    Extended criticality, phase spaces and enablement in biology

    Chaos, Solitons & Fractals

    Biological evolution entails continual changes of the pertinent phase space, leading to unpredictability. We discuss causality as enablement by constraints.


    This paper analyzes, in terms of critical transitions, the phase spaces of biological dynamics. The phase space is the space where the scientific description and determination of a phenomenon is given. We argue that one major aspect of biological evolution is the continual change of the pertinent phase space and the unpredictability of these changes. This analysis will be based on the theoretical symmetries in biology and on their critical instability along evolution. Our hypothesis deeply modifies the tools and concepts used in physical theorizing, when adapted to biology. In particular, we argue that causality has to be understood differently, and we discuss two notions to do so: differential causality and enablement. In this context constraints play a key role: on one side, they restrict possibilities, on the other, they enable biological systems to integrate changing constraints in their organization, by correlated variations, in un-prestatable ways. This corresponds to the formation of new phenotypes and organisms.

    Keywords: Conservation properties, symmetries, biological causality, phase space, unpredictability, phylogenetic drift, enablement

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