The quantum equations of life: Powered by entropy?

Abstract

The title is posed as a question, not because there is any debate as to whether life is powered by entropy,  but because it has not been clear up to now how interesting,  helpful,  or fruitful this idea may be. Since 2019 a new mathematical framework with powerful tools has become available [ref.1] that may make it possible to apply thermodynamics more easily to aspects of living systems.  This Seminar aims to explain these tools in a way that highlights their application to quantum systems. In particular, the tools are based on an entropic Hamiltonian/Lagrangian mathematical framework, which considers two types of entropy: kinetic entropy (KE) and potential entropy (PE). Their sum, the entropic Hamiltonian, is (as is conventional) a system invariant, with the dynamic interplay between the KE and PE as a system evolves determining its key entropic features. Entropy is intrinsically scaleless and the hyperbolic nature of the entropic mathematical framework handles this in a natural fashion. We see this in the molecular-biological progression of Maximum Entropy (MaxEnt) structures from the double-helix of DNA at the primary scale, through to the helices and spherical structures [ref.2] present at secondary, tertiary and quaternary scales. Even at macroscopic scales we continue seeing MaxEnt structures in living entities.  The Nautilus shell, sunflower heads, and romanesco broccoli are all instances of the double logarithmic spiral (as are also spiral galaxies):  this ubiquitous geometry also having been proved MaxEnt [ref.1]. Living bodies are non-equilibrium structures surfing at the edge of order/disorder and chaotic/deterministic behaviour, and understanding the role of entropy in analysing the phenomenon of life is a highly ambitious endeavour. However, we believe that the entropic tools forming the basis for a systematic, mathematical approach towards quantum biology are now beginning to emerge.

1. M.C.Parker, C.Jeynes, Maximum Entropy (Most Likely) Double Helical and Double Logarithmic Spiral Trajectories in Space-Time,  Scientific Reports 9 (2019) 10779 (10 pp,  44 pp Appendices); http://dx.doi.org/10.1038/s41598-019-46765-w 

2. M.C.Parker, C.Jeynes,  Fullerene Stability by Geometrical Thermodynamics,  ChemistrySelect 5 (2020) 5-14;  http://dx.doi.org/10.1002/slct.201903633