This book mathematically analyzes the basic problems of biology, decision making and psychology within the framework of the theory of open quantum systems.

In recent years there has been an explosion of interest in applications of quantum theory in fields beyond physics. The main areas include psychology, decision-making, economics, finance, social science as well as genetics and molecular biology. The corresponding models are referred to as quantum-like; they don’t concern any genuine physical processes in the human brain.

Quantum-like models reflect the special features of information processing in biological, cognitive, and social systems which match well with the quantum formalism. This formalism gives rise to the quantum probability model (QP) which differs essentially from Kolmogorov's classical probability model. QP also serves as the basis for quantum information theory.

Recently QP has been widely applied to the resolution of the basic paradoxes ofdecision making theory and to modeling experimental data stemming from cognition, psychology, economics, and finance thereby shedding light on probability fallacies and irrational behavior.

In this book, the theory of quantum instruments and the quantum master equation are applied to the modeling of biological and cognitive processes, in particular, to the stability of complex biological and social systems interacting with their environment. An essential part of the book is devoted to the theory of the social laser and the Fröhlich condensate.

Table of Contents

Part I Quantum-Like Modeling

1 Interplay Between Classical and Quantum Probability

2 Quantum Formalism for Decision-Making

3 Classical Versus Quantum Rationality

Part II Biosystems as Open Quantum-Like Systems

4 What is Life? Open Quantum Systems Approach

5 Order Stability in Complex Biosystems

6 Brain Functioning

7 Emotional Coloring of Conscious Experiences

Part Ill Quantum Instruments in Psychology and Decision-Making

8 Quantum Instruments and Positive Operator Valued Measures

9 Question Order and Response Replicability Effects

10 Psychological Effects and QQ-equality

Part IV Analysis of Social Systems within Open Quantum System Theory

11 Social Laser

12 Stability in Biological, Ecological, and Social Systems via Frohlich Condensation

13 Social Laser and Networks Within Mean Field Theory

Part V Boundaries of Applicability of Quantum-Like Modeling

14 No-Go Theorem for Modeling with Von Neumann Observables

15 Probabilistic Structure of Cognition: May Be Even Worse than Quantum?

Part VI Foundations and Mathematics

16 Formalism of Quantum Theory

17 Contextuality, Complementarity, and Bell Tests

18 Quantum Statistics from lndistinguishability

Part VII Supplement on Decision-Making

19 Classical Expected Utility Theory and Its Paradoxes

20 Belief State Interpretation

21 God as Decision Maker and Quantum Bayesianism

About the Author

Andrei Khrennikov was born in 1958 in Volgorad and spent his childhood in town Bratsk, in Siberia, north from the lake Baikal. In the period 1975-1980 he studied at Moscow State University, department of Mechanics and Mathematics and then in 1983 obtained his PhD in mathematical physics. Since 1997 he has been professor at Linnaueus University, Sweden, and, since 2002, the director of the multidisciplinary research center, International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science. The research interests of Prof Khrennikov are also characterized by multi-disciplinarity, and include, among others foundations of quantum physics and quantum information, foundations of probability, cognitive modeling, ultrametric (non-Archimedean) mathematics, dynamical systems, quantum-like models in psychology, economics and finances, social and political sciences. He is the author of about 400 papers and 20 monographs. Andrei Khrennikov is theorganizer of the internationally well-known series of annual conferences (held in Växjö since 2000) on the foundations of quantum physics, information, and probability.