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.
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.
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 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 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.
Quantum-like (QL) modeling, one of the outcomes of the quantum information revolution, extends quantum theory methods beyond physics to decision theory and cognitive psychology. While effective in explaining paradoxes in decision making and effects in cognitive psychology, such as conjunction, disjunction, order, and response replicability, it lacks a direct link to neural information processing in the brain. This study bridges neurophysiology, neuropsychology, and cognitive psychology, exploring how oscillatory neuronal networks give rise to QL behaviors. Inspired by the computational power of neuronal oscillations and quantum-inspired computation (QIC), we propose a quantum-theoretical framework for coupling of cognition/decision making and neural oscillations - {\it QL oscillatory cognition.} This is a step, may be very small, towards clarification of the relation between mind and matter and the nature of perception and cognition. We formulate four conjectures within QL oscillatory cognition and in principle they can checkedAsanoexperimentally. But such experimental tests need further theoretical and experimental elaboration. One of the conjectures (Conjecture 4) is on resolution of the binding problem by exploring QL states entanglement generated by the oscillations in a few neuronal networks. Our findings suggest that fundamental cognitive processes align with quantum principles, implying that humanoid AI should process information using quantum-theoretic laws. Quantum-Like AI (QLAI) can be efficiently realized via oscillatory networks performing QIC.
Quantum-like (QL) modeling, one of the outcomes of the quantum information revolution, extends quantum theory methods beyond physics to decision theory and cognitive psychology. While effective in explaining paradoxes in decision making and effects in cognitive psychology, such as conjunction, disjunction, order, and response replicability, it lacks a direct link to neural information processing in the brain. This study bridges neurophysiology, neuropsychology, and cognitive psychology, exploring how oscillatory neuronal networks give rise to QL behaviors. Inspired by the computational power of neuronal oscillations and quantum-inspired computation (QIC), we propose a quantum-theoretical framework for coupling of cognition/decision making and neural oscillations - QL oscillatory cognition. This is a step, may be very small, toward clarification of the relation between mind and matter and the nature of perception and cognition. We formulate four conjectures within QL oscillatory cognition and in principle they can be checked experimentally. But such experimental tests need further theoretical and experimental elaboration. One of the conjectures (Conjecture 4) is on resolution of the binding problem by exploring QL states entanglement generated by the oscillations in a few neuronal networks. Our findings suggest that fundamental cognitive processes align with quantum principles, implying that humanoid AI should process information using quantum-theoretic laws. Quantum-Like AI (QLAI) can be efficiently realized via oscillatory networks performing QIC.
Human reasoning is traditionally modeled through rational-order frameworks that assume stability, separability, and coherence. Yet across judgment, valuation, perception, and social decision-making, empirical work consistently reveals patterned violations of these assumptions. These deviations intensify in real-world contexts shaped by institutional constraints, identity commitments, and collective narratives, where reasoning must navigate incompatible interpretive frames and interdependent evaluative pressures. Existing theories typically treat such phenomena as noise, bias, or bounded rationality, leaving no formal account of how rational-order rules interact with the variability inherent in social domains. This article proposes a structural framework that explains why these two regimes diverge and how their interaction produces systematic mismatches. Building on quantum probability theory, not as a physical metaphor but as a representational tool, it formalizes evaluative states that remain indeterminate until elicited, transform under contextual modulation, and become relationally coupled across agents and domains. Whereas, existing quantum-cognition models primarily address task-level effects such as conjunction errors or order dependence, this framework scales quantum principles to socially and institutionally embedded reasoning. The account identifies contradiction, interference, entanglement, and resolution as recurrent properties of real-world cognition and shows how quantum formalisms provide a coherent vocabulary for capturing these phenomena. To support cumulative progress, the article outlines a research agenda with empirically testable designs for distinguishing incompatible bases, assessing inseparability, modeling context-driven transformations, and integrating multi-level reasoning environments. This program positions quantum and classical approaches within a unified architecture and advances a broader science of reasoning.