By Masanari Asano, Andrei Khrennikov, Masanori Ohya, Yoshiharu Tanaka, Ichiro Yamato
This e-book examines details processing played through bio-systems in any respect scales: from genomes, cells and proteins to cognitive or even social structures. It introduces a theoretical/conceptual precept according to quantum details and non-Kolmogorov chance idea to give an explanation for details processing phenomena in biology as a whole.
The publication starts off with an advent by means of chapters dedicated to basics, one overlaying classical and quantum likelihood, which additionally includes a short advent to quantum formalism, and one other on a data method of molecular biology, genetics and epigenetics. It then is going directly to study adaptive dynamics, together with functions to biology, and non-Kolmogorov chance theory.
Next, the publication discusses the prospect to use the quantum formalism to version organic evolution, particularly on the mobile point: genetic and epigenetic evolutions. It additionally provides a version of the epigenetic mobile evolution in response to the mathematical formalism of open quantum structures. The final chapters of the publication discover foundational difficulties of quantum mechanics and exhibit the ability of utilization of confident operator valued measures (POVMs) in organic science.
This e-book will entice a various staff of readers together with specialists in biology, cognitive technology, choice making, sociology, psychology, and physics; mathematicians engaged on difficulties of quantum chance and knowledge and researchers in quantum foundations.
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Extra info for Quantum Adaptivity in Biology: From Genetics to Cognition
Here the limiting probability distribution ρepi;st describes the probability distribution of epimutations which took place in a cell population as a consequence of interaction with the environment. , to undergo epimutation. 4 Theory of Open Quantum Systems in Biology 31 Internal uncertainty, to epimutate or not epimutate, was resolved and a stable phenotype was created. Finally, we remark that under natural restrictions a selection operator produces the same steady state for all possible initial states, Sect.
6 From Open Quantum System Dynamics to State-Observable Adaptive Dynamics In Sect. 4 we considered the dynamics of the state of a system, say S, interacting with an environment. To derive this dynamics, the Eq. 50), one proceeds in the following framework. The states of the system under consideration are represented in a Hilbert space H and the states of an environment (bath) are represented in another Hilbert space K . Since an environment is a huge system, its state space has very high dimension, in a mathematical model it can be considered as infinite-dimensional.
The state of a classical bi-signal consisting of two components is represented in the Cartesian product of the corresponding L 2 -spaces. , bi-photon, is represented in the tensor product space (Sect. 1). One may state that the crucial difference between the classical and quantum physical models is in the representation of states of compound systems. ) Tensor product, the algebraic definition. Consider now two finite dimensional Hilbert spaces, H1 , H2 . For each pair of vectors ψ ∈ H1 , φ ∈ H2 , we form a new formal entity denoted by ψ ⊗ φ.