Relational Biology

Arturo Tozzi, James Francis Peters, John Steven Torday

The unexploited unification of quantum physics, general relativity and biology is a keystone that paves the way towards a better understanding of the whole of Nature. Here we propose a mathematical approach that introduces the problem in terms of group theory. We build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses the three frameworks as subsets, representing two of their most dissimilar experimental results, i.e., 1) the commutativity detectable both in our macroscopic relativistic world and in biology; 2) and the noncommutativity detectable both in the microscopic quantum world and in biology. This approach leads to a mathematical framework useful in the investigation of the three apparently irreconcilable realms. Also, we show how cyclic groupoids encompassing quantum mechanics, relativity theory and biology might be equipped with dynamics that can be described by paths on the twisted cylinder of a Möbius strip.

Koenraad Kortmulder

Do elements of microstate logic apply to microstate events? What is the relation between macrostate two-valued logic and microstate quantum logic as they reflect deterministic or random events in biology and medicine or even in other fields. The relations between different classifications of probability and logic are not often discussed in the popular literature. It could be especially interesting if random and “chaotic” events in these two realms exhibited identifiable differences affecting outcomes which if more fully understood could have implications for biologic, medical or other fields. Do the two forms of logic reflect identifiable differences in cancer biology?

June Kinoshita

Ginestra Bianconi A, Christoph Rahmede

We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed which is related to a new type of stochastic quantization. We find that the probability distribution of the ensemble of particles can be decomposed into eigenfunctions associated to a discrete spectrum of eigenvalues. In absence of interactions between the particles, the out-of-equilibrium dynamics asymptotically relaxes towards the fundamental state. This phenomenon can be related with the Fisher theorem in biology. On the contrary, in presence of scattering processes the evolution reaches a steady state in which the distribution of the ensemble of particles is characterized by a Bose-Einstein statistics. In order to show a concrete example of this stochastic quantization we have solved explicitly the case in which the potential energy has the harmonic oscillator form.