Temporal Quantum-like Cognition in a Free-Energy Variational Framework.
Entropy (Basel, Switzerland) July 29, 2026 DOI: 10.3390/e28080848 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Keywords | Schrödinger bridge Cognition Consciousness Decision making Free energy principle |
| Key points | Proposes an FEP-inspired, quantum-like variational framework integrating Quantum State Over Time, Schrödinger-bridge theory, and quantum logic, in which cognitive evolution optimizes temporally extended quantum-like states under a composite action. Argues that contextual updating via non-selective Lüders projections and an internal control field can model context-dependent cognitive dynamics, illustrated by a minimal two-state toy model. |
Abstract
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.