Leggett--Garg Tests in Neural Dynamics: Probing Non-Diffusive Stochastic Structure in Single Neurons

• URL: http://arxiv.org/abs/2605.12126v1
• Date: Tue, 12 May 2026 13:49:48 GMT
• Title: Leggett--Garg Tests in Neural Dynamics: Probing Non-Diffusive Stochastic Structure in Single Neurons
• Abstract summary: We show that persistent dynamics can produce oscillatory temporal correlations capable of violating Leggett-Garg inequalities.<n>The resulting temporal correlations indicate persistence, memory, and contextual temporal structure mathematically analogous to that encountered in quantum systems.<n>These tests offer a possible experimental probe of contextual and non-Markovian structure in neural dynamics without requiring claims of microscopic quantum coherence in the brain.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose an experimental programme to test Leggett--Garg-type temporal correlations in single-neuron dynamics. The goal is to distinguish between diffusive (Wiener/cable-equation) models and non-diffusive persistent stochastic models based on Kac-type finite-velocity processes leading to the Telegrapher's equation. We show that while purely diffusive dynamics satisfies Leggett--Garg inequalities, persistent stochastic dynamics can produce oscillatory temporal correlations capable of violating these inequalities. The Leggett--Garg inequality may be viewed as a temporal analogue of Bell-type constraints. In the present context, however, violation is interpreted conservatively not as evidence of microscopic quantum coherence, but as evidence against a simple trajectory-based diffusive description. The resulting temporal correlations indicate persistence, memory, and contextual temporal structure mathematically analogous to that encountered in quantum systems. Using the analytic continuation connecting Kac processes to Dirac-like envelope equations, we argue that finite-velocity persistent stochastic transport provides a natural mechanism for such non-diffusive temporal correlations. These tests therefore offer a possible experimental probe of contextual and non-Markovian structure in neural dynamics without requiring claims of microscopic quantum coherence in the brain.

Related papers

• Topology from Decoherence [39.407739937584104]
  We show that decoherence can induce topological phenomena.<n>We demonstrate this in a lattice system subject to environment-induced dephasing.<n>Our results establish correlated quantum noise as a route to topology in open many-body systems.
  arXiv  Detail & Related papers  (2026-07-08T18:00:04Z)
• Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part II: Prospects for a Trajectory Interpretation [0.0]
  We show that every $Q$-function can be represented as a weighted average of conditional probabilities over boundary values.<n>Despite this limitation, we show that Drummond's trajectory dynamics are fundamentally non-Markovian.
  arXiv  Detail & Related papers  (2026-03-30T20:31:35Z)
• Determinism in the Undetermined: Deterministic Output in Charge-Conserving Continuous-Time Neuromorphic Systems with Temporal Stochasticity [15.346559359976412]
  We develop a unified continuous-time framework for spiking neural networks (SNNs)<n>We prove that this mapping is strictly invariant to spike timing in acyclic networks.<n>We establish an exact representational correspondence between these charge-conserving SNNs and quantized artificial neural networks.
  arXiv  Detail & Related papers  (2026-03-16T23:00:04Z)
• Emergent Manifold Separability during Reasoning in Large Language Models [46.78826734548872]
  Chain-of-Thought prompting significantly improves reasoning in Large Language Models.<n>We quantify the linear separability of latent representations without the confounding factors of probe training.
  arXiv  Detail & Related papers  (2026-02-23T20:36:17Z)
• Non-Markovian Decoherence Times in Finite-Memory Environments [0.0]
  Decoherence is often modeled using Markovian master equations that predict exponential suppression of coherence.<n>Here we formulate decoherence using a general time-nonlocal decoherence functional determined solely by the environmental force correlation function.<n>We show that the decoherence functional exhibits quadratic short-time growth that is model-independent within the finite-memory class considered.
  arXiv  Detail & Related papers  (2026-01-24T09:35:02Z)
• Generalised fractional Rabi problem [35.18016233072556]
  Fractional quantum dynamics provides a natural framework to capture nonlocal temporal behavior and memory effects in quantum systems.<n>In this work, we analyze the physical consequences of fractional-order quantum evolution using a Green's function formulation based on the Caputo fractional derivative.<n>We find that even in the absence of external driving, the static Hamiltonian term induces non-trivial spin dynamics with damping features directly linked to the fractional temporal nonlocality.
  arXiv  Detail & Related papers  (2025-10-09T12:51:57Z)
• Diverse Neural Sequences in QIF Networks: An Analytically Tractable Framework for Synfire Chains and Hippocampal Replay [0.0]
  We propose a parsimonious network of Quadratic Integrate-and-Fire neurons with sequences embedded via a temporally asymmetric Hebbian rule.<n>Our findings demonstrate that this single framework robustly reproduces a spectrum of sequential activities, including persistent synfire-like chains and transient, hippocampal replay-like bursts exhibiting intra-ripple frequency accommodation (IFA)<n>These results establish QIF networks with TAH connectivity as an analytically tractable and biologically plausible platform for investigating the emergence, stability, and diversity of sequential neural activity in the brain.
  arXiv  Detail & Related papers  (2025-08-08T07:27:47Z)
• Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises [37.02662517645979]
  We introduce FANTOM, a unified framework for causal discovery.<n>It handles non-stationary processes along with non-Gaussian and heteroscedastic noises.<n>It simultaneously infers the number of regimes and their corresponding indices and learns each regime's Directed Acyclic Graph.
  arXiv  Detail & Related papers  (2025-06-20T15:12:43Z)
• Neural Persistence Dynamics [8.197801260302642]
  We consider the problem of learning the dynamics in the topology of time-evolving point clouds. Our proposed model - $textitNeural Persistence Dynamics$ - substantially outperforms the state-of-the-art across a diverse set of parameter regression tasks.
  arXiv  Detail & Related papers  (2024-05-24T17:20:18Z)
• Observation of Nonlinear Response and Onsager Regression in a Photon Bose-Einstein Condensate [34.82692226532414]
  The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the temporal response of the average values. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas and, moreover, establishes a test of this relation in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored.
  arXiv  Detail & Related papers  (2024-03-07T17:59:58Z)
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
  In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
  arXiv  Detail & Related papers  (2024-02-14T16:58:21Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.