Difference between revisions of "Store:QLMen14"

We turn to the open system dynamics with the GKSL-equation. In our modeling, Hamiltonian  <math>\widehat{\mathcal{H}}</math> and Lindbladian  <math>\widehat{{L}}</math> represent some special ''biological function'' <math>F</math> (see Khrennikov et al., 2018) for details. Its functioning results from interaction of internal and external information flows. In Sections 10, 11.3,  <math>F</math> is some ''psychological function''; in the simplest case <math>F</math> represents a question asked to  <math>S</math> (say  is a human being). In Section 7, <math>F</math>  is the ''gene regulation'' of glucose/lactose metabolism in Escherichia coli bacterium. In Sections 9, 11.2,  <math>F</math> represents the process of ''epigenetic mutation''. Symbolically biological function <math>F</math> is represented as a quantum observable: Hermitian operator  <math>\widehat{F}</math> with the spectral decomposition <math>\widehat{F}=\sum_xx\widehat{E}^F(x)</math>, where <math>x</math> labels outputs of <math>F</math>. Theory of quantum Markov state-dynamics describes the process of generation of these outputs.

In the mathematical model (Asano et al., 2015b, Asano et al., 2017b, Asano et al., 2017a, Asano et al., 2015a, Asano et al., 2012b, Asano et al., 2011, Asano et al., 2012a), the outputs of biological function <math>F</math>  are generated via approaching a ''steady state'' of the GKSL-dynamics: