Chapter 27
Physics of Biological Oscillators: Outlook
Robert S. MacKay, Aneta Stefanovska, and Constantino Tsallis
Abstract The volume closes with a brief summary of highlights and pointers to
further directions for the physics of biological oscillators.
To understand living systems requires more than just traditional dynamical systems
theory.
Living systems are subject to a time-varying environment, so a key first step is
to use and further develop the theory of non-autonomous dynamical systems. Also,
they do not last forever, so practical versions of dynamical systems concepts like
limit cycles are required that make sense for long but finite time-intervals.
Secondly, a lot of the environment may not be known explicitly, so it is appropriate
to model the residual effects by a stochastic process. There are many candidates,
however, and it is unlikely to be enough to consider only Weiner processes. Many
processes in Nature that serve as perturbations of living systems are in fact oscillatory.
Thirdly, for systems where discreteness plays a role, for example at the level
of biomolecules or at the level of individuals in a population, the dynamics of the
system itself may require a stochastic formulation. Alternatively, individuals in a
population can be treated as oscillatory systems and analysed as networks of coupled
non-autonomous oscillators.
Finally, living systems operate far from thermodynamic equilibrium. Principles
are required to treat this realm of physics. The minimum entropy production rate principle of Glansdorff and Prigogine is valid only near equilibrium. Maes and Netocny
R. S. MacKay (B)
Mathematics Institute and Centre for Complexity Science, University of Warwick, Coventry, UK
e-mail: R.S.MacKay@warwick.ac.uk
A. Stefanovska
Department of Physics, Lancaster University, Lancaster L1 4YB, UK
e-mail: aneta@lancaster.ac.uk
C. Tsallis
Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for
Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ, Brazil
e-mail: tsallis@santafe.edu
© Springer Nature Switzerland AG 2021
A. Stefanovska and P. V. E. McClintock (eds.), Physics of Biological
Oscillators, Understanding Complex Systems,
https://doi.org/10.1007/978-3-030-59805-1_27
423
Physics of Biological Oscillators: Outlook
Robert S. MacKay, Aneta Stefanovska, and Constantino Tsallis
Abstract The volume closes with a brief summary of highlights and pointers to
further directions for the physics of biological oscillators.
To understand living systems requires more than just traditional dynamical systems
theory.
Living systems are subject to a time-varying environment, so a key first step is
to use and further develop the theory of non-autonomous dynamical systems. Also,
they do not last forever, so practical versions of dynamical systems concepts like
limit cycles are required that make sense for long but finite time-intervals.
Secondly, a lot of the environment may not be known explicitly, so it is appropriate
to model the residual effects by a stochastic process. There are many candidates,
however, and it is unlikely to be enough to consider only Weiner processes. Many
processes in Nature that serve as perturbations of living systems are in fact oscillatory.
Thirdly, for systems where discreteness plays a role, for example at the level
of biomolecules or at the level of individuals in a population, the dynamics of the
system itself may require a stochastic formulation. Alternatively, individuals in a
population can be treated as oscillatory systems and analysed as networks of coupled
non-autonomous oscillators.
Finally, living systems operate far from thermodynamic equilibrium. Principles
are required to treat this realm of physics. The minimum entropy production rate principle of Glansdorff and Prigogine is valid only near equilibrium. Maes and Netocny
R. S. MacKay (B)
Mathematics Institute and Centre for Complexity Science, University of Warwick, Coventry, UK
e-mail: R.S.MacKay@warwick.ac.uk
A. Stefanovska
Department of Physics, Lancaster University, Lancaster L1 4YB, UK
e-mail: aneta@lancaster.ac.uk
C. Tsallis
Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for
Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ, Brazil
e-mail: tsallis@santafe.edu
© Springer Nature Switzerland AG 2021
A. Stefanovska and P. V. E. McClintock (eds.), Physics of Biological
Oscillators, Understanding Complex Systems,
https://doi.org/10.1007/978-3-030-59805-1_27
423