Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-11-08
Phys. Rev. E 83, 056104 (2011)
Physics
Condensed Matter
Statistical Mechanics
(8 pages, 1 figure)
Scientific paper
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.
Bianconi Ginestra
Rahmede Christoph
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