arxiv: 2604.18643 · v1 · submitted 2026-04-19 · 🧬 q-bio.NC · quant-ph

Recognition: unknown

Quantum-Like Models of Cognition and Decision Making: Open-Systems and Gorini--Kossakowski--Sudarshan--Lindblad Dynamics

Andrei Khrennikov, Masanari Asano

Pith reviewed 2026-05-10 04:57 UTC · model grok-4.3

classification 🧬 q-bio.NC quant-ph

keywords quantum-like cognitionGKSL dynamicscognitive beatsdecision makingopen quantum systemscognitive agencyPrisoner's Dilemmadissipative evolution

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The pith

Non-commuting Hamiltonians in open quantum models mark cognitive agency by enabling escape from classical equilibria in decisions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a dynamical framework for quantum-like cognition using the Gorini-Kossakowski-Sudarshan-Lindblad master equation to describe mental state evolution as a dissipative process influenced by an informational environment. It demonstrates that non-commutation between the Hamiltonian and decision basis projections indicates active cognitive agency, allowing the system to avoid classical equilibria such as Nash outcomes in strategic games. The framework also identifies cognitive beats as a slow modulation arising from competing Liouvillian channels, which maps the timing of internal conflicts and serves as a diagnostic for deliberation depth. Sympathetic readers would value this because it provides a mathematical structure for understanding why decisions deviate from rational predictions and how internal mental processes unfold over multiple time scales.

Core claim

The central claim is that applying GKSL dynamics to cognition distinguishes passive and active Hamiltonians, with non-commutation serving as the mathematical signature of cognitive agency and quantum escape from classical equilibria. This allows stabilization of non-Nash outcomes in games like the Prisoner's Dilemma. Cognitive beats emerge from structural tension between Liouvillian channels at equal frequencies, generating a secondary slow-scale modulation of conviction that dictates peak readiness and hesitation, offering a spectral diagnostic for the depth of cognitive agency and complexity of deliberation.

What carries the argument

The Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation applied to open quantum systems, particularly the non-commutation of active Hamiltonians with decision projections and the resulting cognitive beats from competing dissipative channels.

Load-bearing premise

The mathematical structures of open quantum systems, including non-commuting Hamiltonians and competing Liouvillian channels, directly correspond to and can be interpreted as features of human cognition and decision processes.

What would settle it

A controlled experiment in the Prisoner's Dilemma where human participants fail to show the predicted stabilization of non-Nash outcomes or lack measurable slow-scale modulations in conviction levels consistent with the cognitive beat model.

Figures

Figures reproduced from arXiv: 2604.18643 by Andrei Khrennikov, Masanari Asano.

**Figure 7.1.** Figure 7.1: 19 [PITH_FULL_IMAGE:figures/full_fig_p019_7_1.png] view at source ↗

**Figure 1.** Figure 1: Cognitive beats. Interpretation in GKSL / QCDM dynamics The appearance of beats indicates the presence of at least two oscillatory modes of the Liouvillian dynamics with nearby imaginary parts of the eigenvalues. The frequencies ω1 and ω2 are determined by the Liouvillian spectrum, while the amplitudes A1 and A2 depend on the projection of the initial state onto the corresponding eigenmodes. Thus the con… view at source ↗

read the original abstract

This paper starts with surveying the evolution of quantum-like models of cognition and decision making, transitioning from static kinematic representations to a robust dynamical framework based on open quantum systems. We provide a comprehensive analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation's application in cognitive psychology and decision making, illustrating how it models mental state evolution as a dissipative process influenced by an informational environment. We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria. The utility of this framework is further explored through its ability to stabilize non-Nash outcomes in strategic games, such as the Prisoner's Dilemma. Building upon this dynamical foundation, we identify ``cognitive beats'' as a signature of the internal struggle between competing ``flows of mind'' deliberated at approximately equal frequencies. Distinct from the damped oscillations of simple interference, these beats emerge from a structural tension between Liouvillian channels that generates a secondary, slow-scale modulation of conviction. This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. By resolving these nested time scales, we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process. This paper develops a theoretical framework linking GKSL dynamics with quantum-like cognition and decision-making (QCDM), highlighting how dissipative quantum models can capture features of human thought and decision processes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adds GKSL open-system dynamics and 'cognitive beats' to quantum-like cognition models, but the agency and escape claims stay mostly interpretive labels rather than derived outcomes.

read the letter

The main takeaway is that this work shifts quantum-like cognition from static pictures to open-system GKSL evolution and introduces cognitive beats as a slow modulation from competing Liouvillian channels. It also splits Hamiltonians into passive and active types, linking non-commutation with decision projectors to agency and escape from classical equilibria, with a side claim that this setup can hold non-Nash outcomes in games like the Prisoner's Dilemma. The survey of earlier static models is straightforward and gives context for the move to dissipative dynamics. The beats idea is presented as a new spectral signature for the depth of internal conflict, distinct from simple interference oscillations. That part is the clearest addition. The framework is laid out in plain terms and the connection to informational environments is consistent with the open-systems approach. The soft spots are in the interpretive steps. Non-commutation is called a signature of agency by definition, and the stabilization of non-Nash states is asserted without a concrete Hamiltonian or solved master equation shown for the Prisoner's Dilemma example. The beats likewise come from structural tension between channels rather than emerging as a calculable feature from specific operators. This makes the cognitive mappings feel assigned rather than forced by the math, and there are no error bounds, parameter fits, or falsifiable predictions attached. The paper stays theoretical, so the lack of data is not a surprise, but the central claims would be stronger with at least one worked example of the dynamics. Readers already working in quantum cognition will find the extension useful as a modeling toolkit and a source of new terminology. A serious referee should see it because the GKSL application is coherent on its own terms and the beats concept is worth checking for whether it adds anything beyond re-labeling existing dissipative effects. I would send it for review with a request for explicit derivations and one solved case to test the escape and beat claims.

Referee Report

3 major / 2 minor

Summary. This manuscript surveys the progression of quantum-like models of cognition and decision making from static kinematic representations to dynamical frameworks based on open quantum systems. It provides an analysis of the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation applied to mental state evolution as a dissipative process. The paper categorizes dynamical regimes into Passive and Active Hamiltonians, interpreting non-commutation with projections on the decision basis as a mathematical signature of cognitive agency that enables Quantum Escape from classical equilibria. It explores the framework's application to strategic games such as the Prisoner's Dilemma for stabilizing non-Nash outcomes. The work further identifies 'cognitive beats' emerging from structural tension between competing Liouvillian channels, generating a secondary slow-scale modulation of conviction that serves as a spectral diagnostic for the depth of cognitive agency and deliberation complexity.

Significance. If the interpretive mappings from GKSL dynamics to cognitive features are supported by explicit derivations, this framework could offer a useful dynamical extension to quantum-like cognition models, potentially capturing agency, internal conflict, and timed deliberation through dissipative evolution and spectral features. The concept of cognitive beats provides a novel angle on nested timescales in decision processes. However, the current significance is constrained by the absence of concrete operator constructions and solved dynamics, limiting immediate applicability or falsifiability.

major comments (3)

[section on strategic games] In the section on strategic games and the Prisoner's Dilemma, the claim that GKSL dynamics stabilize non-Nash outcomes is asserted without the explicit Hamiltonian, Lindblad operators, or the solved master-equation steady-state populations that would demonstrate the non-classical distribution.
[section on cognitive beats] In the section introducing cognitive beats, the emergence of a secondary slow-scale modulation from tension between Liouvillian channels is described without specifying the competing frequencies, the explicit form of the channels, or the derived beat envelope frequency that would support the spectral diagnostic for agency depth.
[categorization of dynamical regimes] In the categorization of dynamical regimes into Passive and Active Hamiltonians, non-commutation with decision-basis projections is presented as the signature of cognitive agency and Quantum Escape, yet no worked example derives how this non-commutation produces escape from classical equilibria in a concrete decision model.

minor comments (2)

The manuscript would benefit from a clearer statement distinguishing the novel elements (such as the cognitive beats diagnostic) from prior surveys of GKSL applications in quantum cognition.
Notation for the GKSL equation and Liouvillian channels should include explicit references to standard forms to aid readability for readers outside the immediate subfield.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript. The comments identify opportunities to strengthen the explicit support for our interpretive framework, and we will revise the paper accordingly to address these points while preserving its survey character.

read point-by-point responses

Referee: In the section on strategic games and the Prisoner's Dilemma, the claim that GKSL dynamics stabilize non-Nash outcomes is asserted without the explicit Hamiltonian, Lindblad operators, or the solved master-equation steady-state populations that would demonstrate the non-classical distribution.

Authors: We agree that the strategic-games section would benefit from greater concreteness. In the revision we will supply explicit forms for the Hamiltonian and Lindblad operators appropriate to the Prisoner's Dilemma, together with the analytic or numerical steady-state solution of the master equation. These additions will directly exhibit the non-classical population distribution and thereby substantiate the stabilization claim. revision: yes
Referee: In the section introducing cognitive beats, the emergence of a secondary slow-scale modulation from tension between Liouvillian channels is described without specifying the competing frequencies, the explicit form of the channels, or the derived beat envelope frequency that would support the spectral diagnostic for agency depth.

Authors: We accept that the cognitive-beats discussion remains at a descriptive level. The revised manuscript will define the two competing Liouvillian channels with their respective frequencies, derive the beat-envelope frequency from their structural mismatch, and show how this frequency serves as the proposed spectral diagnostic. This will make the claimed link between channel tension and deliberation complexity explicit. revision: yes
Referee: In the categorization of dynamical regimes into Passive and Active Hamiltonians, non-commutation with decision-basis projections is presented as the signature of cognitive agency and Quantum Escape, yet no worked example derives how this non-commutation produces escape from classical equilibria in a concrete decision model.

Authors: The categorization is offered as a general mathematical signature, yet we recognize that a concrete derivation would improve accessibility. We will insert a worked example of a simple binary decision task in which the active Hamiltonian is constructed explicitly, its non-commutation with the decision-basis projectors is verified, and the resulting GKSL evolution is solved to demonstrate departure from the classical equilibrium. This example will illustrate the Quantum-Escape mechanism without altering the overall framework. revision: yes

Circularity Check

2 steps flagged

Non-commutation with decision-basis projectors and Liouvillian beats are labeled as signatures of agency by definitional categorization within the GKSL model.

specific steps

self definitional [Abstract]
"We categorize dynamical regimes into Passive and Active Hamiltonians, demonstrating how non-commutation with projections on decision basis serves as a mathematical signature of cognitive agency and Quantum Escape from classical equilibria."

The paper defines the Active/Passive distinction via the commutation property and then asserts that this same property 'serves as' the signature of agency; the claimed mathematical signature is therefore the definition itself rather than a derived consequence.
self definitional [Abstract]
"we identify ``cognitive beats'' as a signature of the internal struggle between competing ``flows of mind'' deliberated at approximately equal frequencies. [...] This beat envelope dictates the timing of peak readiness and hesitation, providing a mathematical map of the transition between conflicting cognitive states. [...] we provide a new spectral diagnostic for the depth of cognitive agency and the complexity of the underlying deliberation process."

The slow modulation arising from competing Liouvillian channels is identified and then immediately labeled as the 'signature' and 'spectral diagnostic' of cognitive agency depth; the interpretive mapping is introduced by the paper's own identification step.

full rationale

The paper's derivation chain begins with standard GKSL mathematics and then categorizes regimes and identifies features (non-commutation as agency signature; beats as diagnostic of deliberation depth) directly within that framework. These interpretive mappings are presented as demonstrated outcomes but reduce to the model's own labeling and structural assumptions rather than independent derivation, empirical fit, or external theorem. No explicit solved dynamics, concrete operators for the Prisoner's Dilemma, or parameter-fitting steps are shown that would allow falsification outside the definitions. This produces moderate circularity confined to the cognitive interpretation layer, while the underlying open-systems formalism remains non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The framework rests on the domain assumption that quantum open-system mathematics can be directly interpreted as cognitive processes, plus ad-hoc interpretive axioms linking non-commutation and Liouvillian competition to agency and beats; no free parameters or invented entities with independent evidence are listed in the abstract.

axioms (2)

domain assumption Mental states evolve according to the GKSL master equation in an informational environment
Foundational premise of the quantum-like cognition approach surveyed in the paper
ad hoc to paper Non-commutation of Hamiltonian with decision-basis projections indicates cognitive agency
Introduced as the mathematical signature of Quantum Escape

invented entities (1)

Cognitive beats no independent evidence
purpose: Signature of internal struggle between competing flows of mind at similar frequencies
New interpretive entity arising from tension between Liouvillian channels

pith-pipeline@v0.9.0 · 5592 in / 1458 out tokens · 46792 ms · 2026-05-10T04:57:46.192642+00:00 · methodology

discussion (0)

Reference graph

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