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