424
R. S. MacKay et al.
[4] have come up with an extension that is valid for all Markov processes, namely
that the stationary distribution maximises the Donsker-Varadhan large deviation rate
function for fluctuations in the occupation probabilities, but more work is required
to make this physically meaningful. See [3] for a recent survey.
Another principle, that goes back to Helmholtz, then Ashby in the days of cybernetics, and has been extended by Friston [2], is the free energy principle. It states
that systems act to minimise “surprise”: the discrepancy between observations and
beliefs. See the Wikipedia page for more. On the other hand, a totally opposite principle has been promoted, the future state maximisation principle, that individuals act
to keep their options open as much as possible (for an application, see [1]).
Although various of the above phenomena in living organisms are describable
within the realm of statistical mechanics and thermodynamics, they cannot be
described in terms of the Boltzmann–Gibbs theory. This is because, in one way
or another, the latter requires the microscopic dynamics to be strongly chaotic, i.e.,
basically mixing and ergodic, being consistently based on the usual additive entropic
functional. Living and living-like organisms and systems (economics, linguistics,
geophysics, astrophysics), with their subtle nature, usually evolve within weak chaos,
at the edge of chaos, between strong chaos and order (typically with vanishing
Lyapunov exponents). This feature usually mandates nonadditive entropic functionals, and, consequently, an entire reformulation and mesoscopic interpretation
of thermodynamics itself (see, for instance, [5]).
This volume has concentrated on the physics of biological oscillations. The pervasiveness of oscillations in living systems suggest that none of the above principles will
really get to the heart of how living systems function. Their dynamical nature must
be taken into account. So also must the continuous exchange of energy and matter,
which is the key characteristic of living systems. It occurs on all scales ranging from
exchange across the cell membrane to exchanges at organ and system levels. So,
conservation of matter (mass) is not an appropriate principle. It is the exchange of
matter that results in the continuous sustained oscillations that are observed, with
frequencies that are non-constant. Perhaps one can focus on the interactions between
different parts of the system to develop new principles based on the phase differences between non-autonomous oscillatory systems, or networks of such systems.
This scenario seems realistic in view of the studies that have already pointed to the
stabilising effect of non-autonomicity.
References
1. H.J. Charlesworth, M.S. Turner, Intrinsically motivated collective motion. PNAS 116, 15362–
15367 (2019)
2. K. Friston, The free-energy principle: a unified brain theory? Nat. Rev. Neurosci. 11, 127–138
(2010)
3. C. Maes, Frenesy. https://arxiv.org/abs/1904.10485
4. C. Maes, K. Netocny, Minimum entropy production principle from a dynamical fluctuation law.
J. Math. Phys. 48, 053306 (2007)
5. C. Tsallis, Beyond Boltzmann-Gibbs-Shannon in physics and elsewhere. Entropy 21, 696 (2019)
R. S. MacKay et al.
[4] have come up with an extension that is valid for all Markov processes, namely
that the stationary distribution maximises the Donsker-Varadhan large deviation rate
function for fluctuations in the occupation probabilities, but more work is required
to make this physically meaningful. See [3] for a recent survey.
Another principle, that goes back to Helmholtz, then Ashby in the days of cybernetics, and has been extended by Friston [2], is the free energy principle. It states
that systems act to minimise “surprise”: the discrepancy between observations and
beliefs. See the Wikipedia page for more. On the other hand, a totally opposite principle has been promoted, the future state maximisation principle, that individuals act
to keep their options open as much as possible (for an application, see [1]).
Although various of the above phenomena in living organisms are describable
within the realm of statistical mechanics and thermodynamics, they cannot be
described in terms of the Boltzmann–Gibbs theory. This is because, in one way
or another, the latter requires the microscopic dynamics to be strongly chaotic, i.e.,
basically mixing and ergodic, being consistently based on the usual additive entropic
functional. Living and living-like organisms and systems (economics, linguistics,
geophysics, astrophysics), with their subtle nature, usually evolve within weak chaos,
at the edge of chaos, between strong chaos and order (typically with vanishing
Lyapunov exponents). This feature usually mandates nonadditive entropic functionals, and, consequently, an entire reformulation and mesoscopic interpretation
of thermodynamics itself (see, for instance, [5]).
This volume has concentrated on the physics of biological oscillations. The pervasiveness of oscillations in living systems suggest that none of the above principles will
really get to the heart of how living systems function. Their dynamical nature must
be taken into account. So also must the continuous exchange of energy and matter,
which is the key characteristic of living systems. It occurs on all scales ranging from
exchange across the cell membrane to exchanges at organ and system levels. So,
conservation of matter (mass) is not an appropriate principle. It is the exchange of
matter that results in the continuous sustained oscillations that are observed, with
frequencies that are non-constant. Perhaps one can focus on the interactions between
different parts of the system to develop new principles based on the phase differences between non-autonomous oscillatory systems, or networks of such systems.
This scenario seems realistic in view of the studies that have already pointed to the
stabilising effect of non-autonomicity.
References
1. H.J. Charlesworth, M.S. Turner, Intrinsically motivated collective motion. PNAS 116, 15362–
15367 (2019)
2. K. Friston, The free-energy principle: a unified brain theory? Nat. Rev. Neurosci. 11, 127–138
(2010)
3. C. Maes, Frenesy. https://arxiv.org/abs/1904.10485
4. C. Maes, K. Netocny, Minimum entropy production principle from a dynamical fluctuation law.
J. Math. Phys. 48, 053306 (2007)
5. C. Tsallis, Beyond Boltzmann-Gibbs-Shannon in physics and elsewhere. Entropy 21, 696 (2019)