Andrei Khrennikov
Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences, Växjö, SE-351 95, Sweden
Andrei.Khrennikov [at] lnu.se
Abstract
Recently the quantum formalism and methodology started to be applied to modeling of information processing in biosystems, mainly to the process of decision making and psychological behavior (but some applications to microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modeling. In this presentation, we turn to the famous Schrödinger book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed out to order preservation as one of the main distinguishing features of biosystems. Entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preserve the order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment E:
1) entropy (disorder) increasing in the process of adaptation to the specific features of E};
2) entropy decreasing (order increasing) resulting from adaptation;
3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.
Such quantum entropy dynamics is illustrated by graphs obtained via numerical simulation for quantum master equation. For simplicity of modelling we consider only quantum Markov dynamics. But the real dynamics of biosystems’ states is non-Markovean.
Keywords: Open quantum systems, biosystems, order stability, entropy dynamics, quantum master equation, adaptation to environment, camel-like shape of entropy
