Quantum Markers of Brain Processes

• Quantum markers are defined as measurable signatures, such as nuclear spin transitions and tunneling events, that indicate quantum influences in brain dynamics.
• Hybrid frameworks using partial Wigner transforms model both quantum observables and classical variables to capture operator-valued traces in neural systems.
• Advanced techniques like high-sensitivity NMR and quantum metrology serve to experimentally validate these markers as control variables linking microscopic quantum events with macroscopic neural behavior.

Quantum markers of brain processes are defined as physical features, signatures, or measurable characteristics within brain dynamics that indicate the presence or influence of quantum mechanical laws or quantum–like processing at any organizational scale. These may originate from explicit quantum degrees of freedom (e.g., nuclear/electron spins, tunneling states, entangled molecular clusters) or manifest in emergent dynamics (e.g., coherence, context-dependence, irreversible evolution) that can be modeled using quantum–classical formalisms. Recent theoretical advancements conceptualize the brain as a fundamentally dissipative open system, where quantum subsystems are dynamically coupled to a classical environment, and quantum markers emerge both from direct quantum variables and from hybrid dynamical interactions.

1. Quantum–Classical Hybrid Frameworks

The quantum–classical approach posits that a faithful description of brain dynamics requires explicit treatment of both quantum observables (such as operators for nuclear/electron spins, orbital states, or tunneling coordinates) and classical phase-space degrees of freedom (positions and momenta for collective modes) (Sergi et al., 2023, Sergi et al., 18 Feb 2025). This is operationalized via the partial Wigner transform, which yields a Wigner function operator $\tilde f_W(\hat r, X; t)$, where $\hat r$ denotes quantum operators and $X = (R, P)$ represents classical variables.

The system-level Hamiltonian is written as a mixed Weyl symbol: $$H(X, \Upsilon) = \tilde H_S + H_B(X) + H_F(\Upsilon) + \tilde V_{SB}(R) + V_{SEM}(Q)$$ where:

• $\tilde H_S$: quantum subsystem Hamiltonian (e.g., nuclear/electron spins, tunneling states),
• $H_B(X)$: phonon (vibrational mode) Hamiltonian, classical in $(R, P)$,
• $H_F(\Upsilon)$: electromagnetic field Hamiltonian, classical in $(Q, \Pi)$,
• $\tilde V_{SB}(R), V_{SEM}(Q)$: interaction terms coupling quantum and classical modes.

Quantum markers in this framework correspond to persistent operator-valued "traces" in the phase-space evolution, which can back-react and modulate the dynamics of large-scale classical variables.

2. Dissipation, Arrow of Time, and Quantum–Classical Dynamics

Dissipative dynamics are implemented through stochastic (Langevin) or deterministic (Nosé–Hoover chain) mechanisms that model the classical environment as a thermal bath (Sergi et al., 18 Feb 2025). The equations of motion for the hybrid system are constructed using quasi-Lie brackets (QLBs) that blend quantum commutators with classical Poisson brackets: $$\frac{\partial \tilde f_W(\hat r, X; t)}{\partial t} = - \frac{i}{\hbar} ( \tilde h, \tilde f_W(\hat r, X; t) ) + \text{[dissipative terms]}$$ where $(\cdot, \cdot)$ denotes the QLB.

Two notable methods for modeling open-system irreversibility in brain dynamics are:

• Langevin approach: bath coordinates are governed by stochastic differential equations, introducing friction and noise. The classical variables follow:

$$\dot R = \frac{P}{M}, \quad \dot P = -\eta \frac{P}{M} + \frac{F_\alpha(R) + F_{\alpha'}(R)}{2} + \mathcal N(t)$$

with $\mathcal N(t)$ a Gaussian white noise term.

• Nosé–Hoover chain thermostat: temperature control is achieved by coupling auxiliary variables to the physical system, extending phase space and enforcing isothermal conditions.

A crucial feature is that the QLB does not satisfy the Jacobi identity, leading to violation of time-translation invariance. This implies that the hybrid evolution has an intrinsic arrow of time—even if underlying microscopic equations are formally time-reversible, the effective macroscopic evolution is irreversible, in line with the inherently dissipative physiology of brain processes.

3. Quantum Markers: Molecular and Cellular Signatures

Quantum markers are explicitly associated with:

• Nuclear and electron spins: Serve as sources of microscopic quantum coherence. Changes in their state distributions, detected by advanced quantum metrology, are proposed to correlate with brain activities (Sergi et al., 2023, Sergi et al., 18 Feb 2025).
• HOMO/LUMO orbitals of phenyl or indole rings: These are relevant for aromatic amino acids such as tryptophan and phenylalanine, with potential for coherent excitation and superradiance, contributing to non-trivial quantum effects in neural tissue.
• Ion channels and tunneling protons: Non-adiabatic transitions in ions (including proton tunneling) across membrane channels represent direct quantum observables; state reduction in these degrees of freedom can initiate signal-amplifying cascades in macroscopic neurodynamics.
• Composite observables: Operators that depend both on quantum and classical variables—such as phase-space–dependent quantum observables—serve as practical markers, for example, in coupling the quantum state of a spinor to the membrane voltage or field gradient.

A plausible implication is that these quantum markers act as control variables, enabling a minimal set of quantum events to exert amplified influence on the higher-order classical processes in neurons or astrocytic networks—a concept echoed in the "order from order" and quantum amplification mechanisms.

4. Computational Implementation and Simulation

The modeling framework is inherently algorithmic. Time-irreversible quantum–classical dynamics can be simulated efficiently by Brownian dynamics or Nosé–Hoover–Chain thermostatting, providing an arrow of time for open quantum systems in a classical environment (Sergi et al., 18 Feb 2025). This allows the explicit tracking of operator-valued quantities corresponding to quantum markers while capturing classical information flow and dissipation. Key mathematical ingredients include the quantum–classical Liouville equation: $$\frac{\partial \tilde f_W}{\partial t} = -\frac{i}{\hbar}( \tilde h, \tilde f_W ) + \eta \frac{\partial}{\partial P} \left( \frac{P}{M} + \frac{\partial}{\partial (\beta P)} \right) \tilde f_W$$ and the violation of the Jacobi identity (i.e., explicit time irreversibility in the bracket algebra).

By extending these methods to coupled networks of neurons and astrocytes, it becomes possible to investigate how local quantum events—such as spin flips or tunneling transitions—are propagated through and integrated by the macroscopic classical environment, thereby producing observable brain phenomena.

5. Experimental Accessibility and Observable Consequences

The model suggests several experimentally accessible quantum markers:

• Proton spin coherence in brain water may serve as a mediator and reporter of quantum correlations, suitable for observation using high-sensitivity NMR or quantum metrology protocols.
• Superradiant phenomena in tryptophan–aromatic networks and
• Entangled photon emission from C–H bonds in myelin are proposed as macroscopic effects of underlying quantum coherence, notably for long-range synchronization of neural activity.
• Amplification pathways: Quantum resonances or state reduction events that are amplified via the classical (e.g., Hodgkin–Huxley–type) dynamics could manifest as abrupt and irreversible transitions in membrane potentials or collective oscillatory modes.
• Irreversible trajectories: Since the quantum–classical bracket structure imposes an arrow of time, one expects to detect non-equilibrium, path-dependent signatures in physiological recordings (e.g., irreversible local field potential patterns following quantum-initiated events).

Applying this framework to detailed neuronal and astrocytic models holds promise for interpreting experimental data (e.g., from quantum sensors, neuroimaging, or in vitro preparations) with direct reference to quantum markers.

6. Future Directions and Theoretical Extensions

Several goals are outlined for the continued development of quantum–classical brain models:

• Application of these algorithms to simulate coupled molecular and cellular processes, integrating classical neuronal network models with quantum subsystems (e.g., spins, orbitals, tunneling coordinates).
• Quantitative comparison with empirical data, such as measurements from quantum-enhanced electrophysiology or advanced imaging, to confirm or falsify the presence of the predicted quantum markers (Sergi et al., 18 Feb 2025).
• Theoretical refinement of how amplification from quantum events to large-scale classical brain dynamics is realized, clarifying the precise roles of dissipation, non-equilibrium effects, and quantum control pathways.
• Extension to predict and possibly engineer new markers detectable with future quantum sensing technologies.

A plausible implication is that substantiating these models with empirical evidence will clarify how irreducibility and amplification of quantum events underlie critical aspects of cognition, memory formation, neurodynamics, or even the subjective psychological arrow of time.

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In summary, quantum markers of brain processes in a quantum–classical framework are operator-valued quantities—such as nuclear/electron spin observables, coherent orbital modes, or tunneling coordinates—that, through hybrid dissipative dynamics, imprint quantum information on macroscopic neural and astrocytic behavior. Dissipation, arrow of time, and hybrid amplification mechanisms are foundational in bridging the quantum substrate and observable brain-level phenomena, and the modeling approaches described lay the groundwork for future simulations and experimental identification of these markers (Sergi et al., 2023, Sergi et al., 18 Feb 2025).