We review recent theoretical developments linking quantum-like cognition, nonequilibrium thermodynamics, and foundation of quantum mechanics. Empirical studies inpsychology and decision making reveal contextuality, order effects, and violations of classical probability theory that are naturally represented within a Hilbert-space formalism. While quantum-like models clarify how such non-classical structures describe cognitive phenomena, and the Free Energy Principle (FEP) explains why living systems perform variational inference, their conceptual integration has remained incomplete. We here explore a possibility of unifying these concepts in terms of temporally correlated “quantum” states. Reformulating variational free energy as quantum relative entropy, we show that open-system quantum decision models realize a quantum extension of the FEP. Using quantum state-over-time representations, we demonstrate that violations of Leggett–Garg inequalities admit an information-theoretic interpretation as strictly positive lower bounds on a macrorealism-restricted temporal free energy. Extending the framework of thermodynamics of prediction, temporal nonclassicality introduces an additional irreducible energetic cost beyond classical predictive inefficiency. We further examine both material (water–electromagnetic–phonon coherence) and stochastic-network foundations for quantum cognition and decision making, and propose that consciousness may be understood as non-collapsing variational inference sustained by temporally coherent organization in living systems.
We review recent theoretical developments linking quantum-like cognition, nonequilibrium thermodynamics, and foundation of quantum mechanics. Empirical studies inpsychology and decision making reveal contextuality, order effects, and violations of classical probability theory that are naturally represented within a Hilbert-space formalism. While quantum-like models clarify how such non-classical structures describe cognitive phenomena, and the Free Energy Principle (FEP) explains why living systems perform variational inference, their conceptual integration has remained incomplete. We here explore a possibility of unifying these concepts in terms of temporally correlated “quantum” states. Reformulating variational free energy as quantum relative entropy, we show that open-system quantum decision models realize a quantum extension of the FEP. Using quantum state-over-time representations, we demonstrate that violations of Leggett–Garg inequalities admit an information-theoretic interpretation as strictly positive lower bounds on a macrorealism-restricted temporal free energy. Extending the framework of thermodynamics of prediction, temporal nonclassicality introduces an additional irreducible energetic cost beyond classical predictive inefficiency. We further examine both material (water–electromagnetic–phonon coherence) and stochastic-network foundations for quantum cognition and decision making, and propose that consciousness may be understood as non-collapsing variational inference sustained by temporally coherent organization in living systems.
Free-energy-based variational principles provide a powerful framework for describing perception, inference, and decision making. The Free Energy Principle (FEP) is one prominent realization of this idea, but its standard formulation is usually expressed in terms of classical probabilistic generative models. Here, we propose an FEP-inspired, quantum-like variational approach by integrating Quantum State Over Time (QSOT), Schrödinger-bridge (SB) theory, and quantum logic into a unified framework. Cognitive evolution is formulated as the optimization of temporally extended quantum-like states under a composite action consisting of an SB-inspired path divergence, a cognitive free-energy functional, and context-dependent quantum-logical constraints with terminal target propositions. Contextual updating is modeled by time-dependent non-selective Lüders projections, while endogenous cognitive steering is represented by an internal control field. A minimal two-state toy model illustrates how these components jointly shape temporal quantum-like cognitive trajectories. The proposed framework provides a temporally extended quantum-like analogue of the variational structure underlying the FEP and suggests a general mathematical basis for modeling context-dependent cognitive dynamics.
ABSTRACT Recent advances at the intersection of quantum physics, neuroscience, and cognitive science have renewed interest in whether quantum phenomena and quantum‐inspired formalisms can inform models of human cognition and decision‐making. While classical neural and computational models explain many aspects of perception and behavior, they face limitations in accounting for contextuality, order effects, probabilistic reasoning violations, ambiguity resolution, and rapid information integration. This review synthesizes evidence and theoretical frameworks linking quantum‐related principles to cognition, with emphasis on quantum sensing in biological systems, molecular and subcellular quantum‐relevant mechanisms, quantum‐to‐classical transition pathways, quantum‐inspired models of perception and decision‐making, and quantum‐inspired computational approaches. It also extends beyond the probabilistic arm of quantum cognition by considering emerging equilibrium‐based and causal‐logical theories, including mental equilibrium, brain‐universe similarity, mind‐light‐matter unity, quantum emergence, and quantum intelligence. Throughout, the review distinguishes physically instantiated quantum mechanisms from abstract quantum‐like formalisms that model contextuality, mental entanglement, and non‐separable cognitive dynamics without requiring sustained macroscopic quantum coherence in the brain. Finally, it identifies methodological challenges and future directions for advancing quantum cognitive science toward experimentally testable and biologically meaningful theories.
We propose a quantum-mechanical framework to describe the dynamics of human decision making, where the interactions between the open quantum system of decision makers and its surrounding environment at given temperature are relevantly taken into account. The temporal evolution of quantum system is described in terms of the time-dependent density matrix, from which we can evaluate those thermodynamic functions such as internal energy, (von Neumann) entropy and (Helmholtz) free energy. In this study we rely on the symmetrical quasi-classical (SQC) windowing approach to numerically solve the non-adiabatic quantum dynamics. We then consider the Hamiltonians to formulate the Prisoner’s Dilemma (PD) problem and calculate the population dynamics of the quantum states of two players’ decisions, where some quantum coherence or interference effects are observed. The evaluated free energy tends to decrease toward the thermodynamic equilibrium value, thus driving the dynamics of quantum system between the Nash equilibrium and Pareto optimum states. The calculated entropy often shows a tendency of temporal decrease, thus indicating the emergence of order in the quantum system. We have also applied the present scheme to the issue of the violation of the sure thing principle and found its occurrence through explicit numerical simulations for the PD problem. The present study may provide a theoretical basis to connect the dynamics of quantum decision making to the free energy principle in cognitive science.
Abstract The gap between natural and artificial intelligence is often discussed in terms of creativity, contextual adaptability, and non-algorithmic decision-making capacities where human cognition appears fundamentally different from current AI systems. This paper argues that developing quantum and quantum-like models of cognition, decision-making, and AI provides a promising pathway for narrowing, and perhaps essentially bridging, this gap. Empirical studies of human cognition and decision-making reveal systematic deviations from classical probability, logic, and information theory—manifesting as contextuality, order effects, interference (such as conjunction and disjunction effects), task incompatibility, and apparent randomness. These phenomena are well captured by quantum probability theory and related quantum-like frameworks, which provide a rigorous mathematical formalism—Hilbert spaces, superposition, entanglement, and decoherence—for modeling cognitive states and their evolution. Such models go beyond metaphor, showing that aspects of human reasoning can be more faithfully represented using quantum-like rather than classical probabilistic structures. Although genuine quantum (based on quantum physics) and quantum-like approaches share the same mathematical foundation, they differ experimentally. Both stimulate the development of novel AI architectures: quantum AI (QAI) and quantum-like AI (QLAI). While QAI depends on advances in quantum computing, QLAI can be realized on classical digital or analog hardware. The advancement of both offers a promising route to reducing—and potentially bridging—the divide between natural and artificial intelligence. This paper sets out a conceptual program to unify natural and artificial intelligence via quantum/quantum-like models of consciousness/cognition and AI.
Growing empirical evidence reveals that traditional set-theoretic structures cannot in general be applied to cognitive phenomena. This has raised several problems, as illustrated, for example, by probability judgement errors and decision-making (DM) errors. We propose here a unified theoretical perspective which applies the mathematical formalism of quantum theory in Hilbert space to cognitive domains. In this perspective, judgements and decisions are described as intrinsically non-deterministic processes which involve a contextual interaction between a conceptual entity and the cognitive context surrounding it. When a given phenomenon is considered, the quantum-theoretic framework identifies entities, states, contexts, properties and outcome statistics, and applies the mathematical formalism of quantum theory to model the considered phenomenon. We explain how the quantum-theoretic framework works in a variety of judgement and decision situations where systematic and significant deviations from classicality occur.
Quantum theory has inspired many new ideas for understanding Cognition and decision making. Given the nascent state of this field, many new challenges still remain. What are the strengths and unique contributions of these ideas? What are likely next steps in its development? How can it be applied to practical problems in cognitive science? Is this a rational or an irrational system of reasoning? What, if any, are its connections to neuroscience? Should the hard problem of consciousness be considered? These are questions that we try to address in this chapter, albeit at times in a limited way. We end with a debate with a fictitious skeptic (actually previous reviewers) of these ideas. Let us start by reviewing what we have covered so far. Contributions to cognition and decision We begin by summarizing the conclusions reached in previous chapters regarding the usefulness of quantum theory for modelling phenomena in cognition and decision. Chapter 1 provided some motivation and Chapter 2 provided a theoretical introduction to quantum theory. Chapter 3 presented a quantum model to account for question order effects on survey research. An exact and parameter-free test was derived from the model, which produced surprisingly accurate predictions for results obtained from three different large Gallup poll survey studies. Chapter 4 described a quantum model of probability judgments to account for findings that produce violations of classic probability theory, including conjunction and disjunction fallacies and order effects on inference.