Related papers: Quantum mechanical formalism for biological evolut…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
Quantum simulations constructing probability tensors of biological multi-taxa in phylogenetic trees are proposed, in terms of positive trace preserving maps, describing evolving systems of quantum walks with multiple walkers. Basic…
We analyze the time evolution describing a quantum source for noninteracting particles, either bosons or fermions. The growth behaviour of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for…
How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…
The phenomenological evidence of quantum statistical effects in parton physics is here briefly summarized, and the recent good results obtained by parameterizing the parton distributions in terms of Fermi-Dirac and Bose-Einstein statistical…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
A proper understanding of the links between varying gene expression levels and complex trait adaptation is still lacking, despite recent advances in sequencing techniques leading to new insights on their importance in some evolutionary…
Several theoretical frameworks have been proposed to explain observed biodiversity patterns, ranging from the classical niche-based theories, mainly employing a continuous formalism, to neutral theories, based on statistical mechanics of…
The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
In our previous studies, we developed discrete-space Birth, Death and Innovation Models (BDIM) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
We consider an asexual biological population of constant size $N$ evolving in discrete time under the influence of selection and mutation. Beneficial mutations appear at rate $U$ and their selective effects $s$ are drawn from a distribution…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
Research in quantitative evolutionary genomics and systems biology led to the discovery of several universal regularities connecting genomic and molecular phenomic variables. These universals include the log-normal distribution of the…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
We study the behavior of Quantum Darwinism (Zurek, [8]) within the iterative, random unitary operations qubit-model of pure decoherence (Novotny et al, [6]). We conclude that Quantum Darwinism, which describes the quantum mechanical…