| name | gksl-quantum-cognition |
| description | GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation methodology for quantum-like models of cognition and decision making. Models mental state evolution as dissipative process influenced by informational environment. Includes cognitive beats analysis, Passive/Active Hamiltonian regimes, and non-Nash equilibrium stabilization. Use when: quantum cognition, decision making models, open quantum systems in psychology, GKSL/Lindblad equations for cognition, cognitive beats, Prisoner's Dilemma quantum models, ArXiv:2604.18643, quantum-like decision making, Asano Khrennikov.
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GKSL Quantum Cognition Framework
Model cognition and decision making using the GKSL (Lindblad) master equation
from open quantum systems theory.
GKSL Master Equation for Cognition
Mental state ρ evolves as:
dρ/dt = -i[H, ρ] + Σ_k (L_k ρ L_k† - ½{L_k†L_k, ρ})
Where H encodes cognitive dynamics and L_k are Lindblad operators modeling
environmental (informational) influence.
Dynamical Regimes
| Regime | Hamiltonian | Cognitive Meaning |
|---|
| Passive | H commutes with decision basis | Habitual/automatic responses |
| Active | H does NOT commute with decision basis | Cognitive agency, deliberation |
Key diagnostic: Non-commutation with projections on decision basis =
mathematical signature of cognitive agency and quantum escape from classical equilibria.
Cognitive Beats
When competing "flows of mind" operate at approximately equal frequencies:
- Beats emerge from structural tension between Liouvillian channels
- Beat envelope dictates timing of peak readiness and hesitation
- Distinct from simple damped oscillations — secondary slow-scale modulation
- Provides spectral diagnostic for depth of cognitive agency
Applications
Strategic Games (e.g., Prisoner's Dilemma)
GKSL framework can stabilize non-Nash outcomes by modeling the deliberation
process as a dissipative quantum evolution rather than static equilibrium.
Decision Dynamics Pipeline
- Define decision basis (orthogonal outcome states)
- Construct H encoding preferences and conflicts
- Add Lindblad operators for environmental/informational coupling
- Solve for ρ(t) — track conviction oscillations
- Identify beat frequencies → predict hesitation/commitment timing
Nested Timescales
The framework resolves nested temporal structure:
- Fast: Liouvillian channel dynamics (ms-scale neural)
- Beat envelope: Modulation of conviction (s-scale deliberation)
- Decision commitment: Collapse to outcome (behavioral response)
Activation Keywords
GKSL, Lindblad, Gorini Kossakowski Sudarshan, quantum cognition, open quantum
systems cognition, cognitive beats, quantum decision making, Asano, Khrennikov,
non-Nash equilibrium, Prisoner's Dilemma quantum
