Open Quantum Systems in Biology, Cognitive and Social Sciences

Description

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 of decision 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.  Preface Acknowledgments Contents Part I Quantum-Like Modeling 1 Interplay Between Classical and Quantum Probability 1.1 Quantum-Like Models: Motivation 1.2 Briefly About Classical and Quantum Probabilities 1.3 Interference of Probabilities 1.4 Bayesian Versus Non-Bayesian Inference 1.5 Quantum-Like Paradigm: Contextual Information Processing 2 Quantum Formalism for Decision-Making 2.1 Elementary Quantum Vocabulary 2.2 Quantum-Like Model for Decision-Making 2.3 Decision-Making via Decoherence 2.4 Decision Paradoxes 3 Classical Versus Quantum Rationality 3.1 Savage Sure Thing Principle and Interference of Probabilities 3.2 Quantum-Like Rationality 3.3 Coupling of Social Lasing to Deprivation of Classical Rationality 3.4 Question Order and Response Replicability Effects 3.5 State-Dependent Incompatibility Part II Biosystems as Open Quantum-Like Systems 4 What is Life? Open Quantum Systems Approach 4.1 Schrödinger About Life 4.2 Theory of Open Quantum Systems and Order in Biosystems 4.3 Supplement to Elementary Quantum Vocabulary 4.3.1 Superoperators and Quantum Channels 4.3.2 Von Neumann Entropy 4.3.3 Isolated System: Schrödinger and Von Neumann Equations 4.4 Open Quantum Systems 4.5 Gorini-Kossakowski-Sudarshan-Lindblad Equation 4.5.1 Stabilization to Steady State 4.5.2 Quantum Markov Dynamics 4.6 Camel-Like Dynamics of Quantum Entropy 4.7 Open Systems Generating Disorder 4.8 Dynamics of Linear Entropy (Decoherence) 4.9 Specialty of Biosystem's States and Dynamics 4.10 Adaptation to the Environment: Illustrative Examples 5 Order Stability in Complex Biosystems 5.1 Biosystem: Global Order from Local Disorder 5.2 Compound Classical System: Local and Global Orders 5.3 Compound Quantum System: Global and Local Orders 5.4 Global Order from Local Disorder 5.5 Complex Biosystems 5.6 Concluding Discussion: Order Stability in Bio and AI Systems 6 Brain Functioning 6.1 Psychic Versus Physical Phenomena 6.2 From Electrochemical Uncertainty in Action Potentials to Quantum Superposition 6.3 Electrochemical and Quantum Information States: Nonlinear Versus Linear Dynamics 6.4 Quantum Physics of Brain's Functioning: Impossibility of Superposition … 6.5 Mental Function as Decoherence Machine 6.6 Model 1: Collapse of Mental Wave 6.7 Model 2: Open Quantum System Dynamics 6.7.1 General Quantum Dynamics of Mental State 6.7.2 Critical Analysis of Open Quantum System Approach to Cognition 6.8 Model 3: Differentiation of Mental State 6.8.1 Signatures of Environments in a Density Operator 6.8.2 Mathematical Scheme of Differentiation Process 6.9 Autopoiesis: Quantum Information Representation 6.10 Entanglement: Physics Versus Cognition 6.11 Ontic and Epistemic Portrayals of Mental Processes 6.12 Concluding Discussion on Quantum-Like Modeling of Brain's Functioning 7 Emotional Coloring of Conscious Experiences 7.1 Quantum Formalization of Emotional Coloring of Conscious Experiences 7.2 The First and Higher Order Theories of Consciousness 7.3 Contextuality of The Higher Order Theory of Consciousness 7.4 Perceptions and Emotions 7.5 Unconscious and Conscious Information Processing 7.5.1 Unconsciousness as System 7.5.2 Consciousness as Observer 7.5.3 Unconscious and Conscious Generation of Perceptions and Emotions 7.5.4 Conscious Experiences: Basic and Supplementary 7.6 Incompatible Conscious Observables 7.7 Degeneration Resolution of Conscious Experiences via Contextual Coloring 7.8 Tensor Product Decomposition of Unconscious State Space 7.9 CHSH Inequality: Test of Emotional Contextuality 7.10 Concluding Remarks on Emotional Coloring Part III Quantum Instruments in Psychology and Decision-Making 8 Quantum Instruments and Positive Operator Valued Measures 8.1 Von Neumann Observables and von Neumann-Lüders Instruments 8.2 Davis–Lewis–Ozawa Quantum Instruments 8.3 Positive Operator Valued Measures 8.4 Quantum Instruments from Indirect Measurements 8.5 Naimark Theorem 9 Question Order and Response Replicability Effects 9.1 Quantum Instruments for Questions 9.2 Questions as Indirect Measurements 9.2.1 Von Neumann Observables for Questions 9.2.2 Quantum a-Instrument 9.2.3 Quantum Algorithm for Decision-Making 9.2.4 Quantum b-Instrument 9.3 Combination of Order and Response Replicability Effects 9.3.1 Stability of Question Order Effect 9.3.2 Non-atomicity of Instruments 10 Psychological Effects and QQ-equality 10.1 Question Order and Response Replicability Effects and QQ-equality 10.1.1 Observables, Belief and Personality States 10.1.2 Instrument Measuring a-Observable 10.1.3 Instrument Measuring b-Observable 10.2 Generalization of Wang–Busemeyer Postulates 10.3 Mind State Transformations 10.4 Response Replicability Effect: Personality States 10.5 Question Order Effect: Personality States 10.6 Matching with QQ-equality 10.7 Linking Experimental and Theoretical Data 10.8 Independence of Belief and Personality States 10.9 Modeling Statistical Data from Clinton–Gore Poll 10.10 On Postulate 5QL Part IV Analysis of Social Systems within Open Quantum System Theory 11 Social Laser 11.1 Social-Information Waves Shaking the World 11.2 Social Atom 11.3 Social Energy 11.4 Social-Information Field 11.5 Absorption and Emission of Infons by Social Atom 11.6 Social and Physical Lasers 11.7 Echo Chamber: Social Coherence Reinforcing 11.8 Illustrating Examples 11.9 Technical Details 11.10 Social Spin 11.11 Concluding Remarks On Social Laser 12 Stability in Biological, Ecological, and Social Systems via Fröhlich Condensation 12.1 Modeling of Fröhlich Condensation 12.1.1 Coherent Vibrations in Biomolecules and Cells 12.1.2 Long-Range Nonlinear Interactions 12.1.3 Quantum-Like Modeling of Fröhlich Condensation 12.1.4 Fröhlich Condensation of Information Excitations 12.2 Review on Fröhlich's Works 12.3 Conditions for Fröhlich Condensation 12.4 Quantum Formalism for Fröhlich Condensation 12.5 Cancer 12.6 Condensation of Information 12.7 Information Temperature 12.8 Stability of Complex Information Societies 12.9 Order in Pack of Wolfs 12.10 Concluding Remarks on Physical and Social Fröhlich Condensation 13 Social Laser and Networks Within Mean Field Theory 13.1 Social Networks: Laser Physics, Phase Transition, and Critical Phenomena 13.2 Ising Model for Complex Networks: Equilibrium Phase Transition 13.2.1 Ising-Type Interaction ín Networks 13.2.2 Phase Transition and Network's Structure 13.3 Non-equilibrium Phase Transition in Social Laser 13.3.1 Primary Consideration 13.3.2 Social Laser: Mean Field Framework 13.3.3 Social Laser: Phase Transition 13.4 Social Laser Dynamics and Information Spread 13.4.1 Viral Information Cascades in Social Laser 13.4.2 Velocity of Information Reinforced 13.5 Concluding Discussion on Social Laser and Networks Part V Boundaries of Applicability of Quantum-Like Modeling 14 No-Go Theorem for Modeling with Von Neumann Observables 14.1 Sequential Measurements in Physics and Psychology 14.2 Von Neumann Observables and Unitary Inter-measurement Evolution 14.3 Measurement Sequences: Evolution (In)Effectiveness and Stability 14.4 Measurement Sequences a rightarrowa 14.5 Measurement Sequences a rightarrowb rightarrowa 15 Probabilistic Structure of Cognition: May Be Even Worse than Quantum? 15.1 Comparing Foundations of Quantum Physics and Cognition 15.2 Abstract Presentation for Sorkin's Equality 15.3 Derivation of Sorkin's Equality 15.4 Emigration Experiment 15.5 Triple-Store Experiment in Economics Part VI Foundations and Mathematics 16 Formalism of Quantum Theory 16.1 Mathematical Structure of Quantum Theory 16.2 Quantum Mechanics as Axiomatic Theory 16.3 Projection Postulate: Von Neumann Versus Lüders Forms 16.4 Classical Probability: Kolmogorov Axiomatics 16.5 Quantum Conditional Probability 16.6 Derivation of Interference of Probabilities 16.7 Compatible Versus Incompatible Observables 16.8 Quantum Logic 16.9 Tensor Product 16.10 Symbolism of Ket- and Bra-Vectors 16.11 Qubit 16.12 Entanglement 17 Contextuality, Complementarity, and Bell Tests 17.1 Preliminary Discussion 17.2 Växjö Model 17.3 Thinking over Bohr's Ideas 17.3.1 Bohr Contextuality 17.3.2 Bohr's Principle of Contextuality-Complementarity 17.4 Probabilistic Viewpoint on Contextuality-Complementarity 17.5 Clauser, Horne, Shimony, and Holt (CHSH) Inequality 17.6 CHSH-Inequality for Quantum Observables 17.7 Signaling in Physical Versus Psychological Experiments 17.8 Contextuality-by-Default 17.9 Mental Signaling: Fundamental or Technical? 17.10 Sources of Signaling Compatible with Quantum Formalism 17.11 Meal Choice Experiment: Possible Source of Signaling 17.12 Concluding Remarks on Cognitive Tests with Bell Inequalities 17.13 Joint Measurement Contextuality 17.14 Contextual Resolution of Degeneration of Eigenvalues of Observables 18 Quantum Statistics from Indistinguishability 18.1 Thermodynamics from Gibbs Ideal Ensembles 18.2 Distinguishable Systems: Classical Statistics 18.3 Indistinguishable Systems: Quantum Statistics 18.4 Classical and Quantum statistics Part VII Supplement on Decision-Making 19 Classical Expected Utility Theory and Its Paradoxes 19.1 Von Neumann and Morgenstern: Expected Utility Theory 19.2 Allais Paradox 19.3 Savage: Subjective Expected Utility Theory 19.4 Ellsberg Paradox 19.5 Quantum-Like Modeling of Subjective Expected Utility 20 Belief State Interpretation 20.1 The Spirit of Copenhagen 20.2 Interpretations: Statistical Versus Individual 20.3 QBism: Subjective Interpretation 20.4 Växjö Interpretation 21 God as Decision Maker and Quantum Bayesianism 21.1 Bohr Versus Bell 21.2 Supplement on Quantum Bayesianism (QBism) 21.3 QBism Versus Copenhagen Interpretation 21.4 Free Will Given by God to Adam is the Source of Irreducible Uncertainty in the Universe 21.5 God as Decision Maker Operating with Subjective Probability Assigned … Appendix A Technicalities A.1 Proof of Theorem 4.7.1 Chap. 4 A.2 Construction of Quantum Channels A.2.1 Two Subsystems with Qubit State Spaces A.2.2 Two Subsystems with N-dimensional State Spaces A.3 Signaling from Contextual State Modification References Index