gksl-quantum-cognition

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.

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

1. Define decision basis (orthogonal outcome states)
2. Construct H encoding preferences and conflicts
3. Add Lindblad operators for environmental/informational coupling
4. Solve for ρ(t) — track conviction oscillations
5. 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