# The Mechanics Underpinning Non-Deterministic Computation in Cortical Neural Networks

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Modeling the Cortical Neuron as a Two-State Quantum System

_{0}to t, the state of the neuron evolves from $\varphi $ to $\chi $. The timepath taken from one state to another is given by:

_{k}and C

_{j}. The sum of the squared moduli of all probability amplitudes is equal to 1:

#### 2.2. Modeling the Cortical Neuron Membrane Potential as a Function of Component Pure States

#### 2.3. Modeling the Information Encoded by the Multi-State System, in Terms of von Neumann Entropy

#### 2.4. Generating a Distribution of Possible System States from Quantum Uncertainty

#### 2.5. Reducing the Probability Distribution into a Single Observable System State

#### 2.6. Restoring Uncertainty after the System State Is Transiently Defined

#### 2.7. Converting Probabilistic System States to Temporally Irreversible Signaling Outcomes

#### 2.8. Conditions under Which Quantum Fluctuations Contribute to Dissipation Dynamics

#### 2.9. Assumptions of the Model

#### 2.9.1. Neurons Are Functionally Isolated but Remain Sensitive to External Perturbations

#### 2.9.2. Uncertainty in the State of Individual Ions Affects the Voltage State of the Neuron

#### 2.9.3. The Estimated Decoherence Timescales Meet the Criteria for a Quantum System

## 3. Results

#### 3.1. The Expected Wavelength of Spontaneous Free Energy Release during Information Compression

^{12}Hz, a wavelength of $\lambda $ < 46 microns, or an energy of E > 0.0267 eV, within the infrared light spectrum. Spontaneous emissions of photons in this range have indeed been observed in mammalian brain tissue [52,53,54,55] and infrared stimulation of the brain has been shown to have a functional effect on neural activity [56,57,58]. Further studies are needed to measure the exact wavelengths of these photon emissions and temporally correlate these events with neuronal signaling outcomes.

#### 3.2. Specific Predictions of This Model

#### 3.2.1. Thermal Free Energy Is Spontaneously Released during Computation as Information Is Compressed

^{12}Hz should spontaneously appear at the neural membrane during cortical information processing. This prediction must be tested with sensitive infrared detection devices rather than classical electrodes or imaging systems; the spontaneous release of infrared-wavelength particles should be observed in the brain as uncertainty is resolved into signaling outcomes. A quantitative increase in these particles should be observed, for example, upon perceptual recognition of a highly uncertain visual or auditory stimulus, with a strong temporal correspondence to P300 event-related potentials in the cerebral cortex. By contrast, this spontaneous thermal free energy release should not occur in the case of an epileptic seizure—when constitutive ion channel activation, rather than information processing, leads to highly synchronized neural activity across the cerebral cortex. Of course, spontaneous emissions of photons in this range have been observed in mammalian brain tissue [52,53,54,55], and infrared stimulation of the brain has been shown to have a functional effect on neural activity [56,57,58], but further studies are needed to measure the exact wavelengths of these photon emissions and evaluate whether these events are temporally correlated with neuronal signaling outcomes. If the brain does cyclically generate and compress entropy, the system should demonstrate much higher energy efficiency than expected under classical conditions (Table 1).

#### 3.2.2. The Spontaneous Release of Thermal Free Energy during Information Compression Prompts Synchronized Firing across the Neural Network

## 4. Discussion

## Funding

## Data Availability Statement

## Conflicts of Interest

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Classical models | ||

Proposed Mechanism | Predicted Observation | Evidence For/Against |

The energy efficiency of the system is the result of optimal synaptic weighting, optimal ion channel distribution, and other molecular mechanisms. | Net production of physical entropy in the human brain is compatible with classical assumptions, with ATP turnover producing some amount of entropy. | The computational cost for each spike is an astounding 0.1 W: In the context of known caloric intake, this energy requirement is “off by a factor of ${10}^{8}$.” [60] |

Present model | ||

Proposed Mechanism | Predicted Observation | Evidence For/Against |

The energy efficiency of the system is the result of information compression, with neural outcomes prompted by the extraction of correlations, consistencies, or ‘predictive value’. | Net production of physical entropy in the human brain is far too low to retain the assumptions of a classical system, with the amount of work done per calorie showing near-perfect use. | “The energy efficiency of the human brain is consistent with this model of non-deterministic computation.” [17] “This computational process maximizes free energy availability.” [26] |

Classical models | ||

Proposed Mechanism | Predicted Observation | Evidence For/Against |

The observed synchronous firing at a range of nested frequencies is the result of information encoding, with neural signaling outcomes prompted by a common stimulus. | A combination of gap junctions, chemical synapses, ephaptic coupling, changes in ion concentration, and optimization of neural connectivity over time prompts synchronous firing. | These events are not readily simulated: “It is difficult, however, to identify the exact contribution of each mechanism to a specific type of oscillation.” [65] The problem is “non-trivial.” [66] |

Present model | ||

Proposed Mechanism | Predicted Observation | Evidence For/Against |

The observed synchronous firing at a range of nested frequencies is the result of information compression, with neural signaling outcomes prompted by the extraction of correlations. | An infrared photon pulse drops the membrane potential of some neurons, while other neurons in cortical up-state fire, resulting in synchronous firing but not ictal activity across the network. | The predictions of this model should be tested: specifically, spontaneous infrared photon release is expected to be temporally correlated with neural oscillations, but not with ictal activity. |

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Stoll, E.A.
The Mechanics Underpinning Non-Deterministic Computation in Cortical Neural Networks. *AppliedMath* **2024**, *4*, 806-827.
https://doi.org/10.3390/appliedmath4030043

**AMA Style**

Stoll EA.
The Mechanics Underpinning Non-Deterministic Computation in Cortical Neural Networks. *AppliedMath*. 2024; 4(3):806-827.
https://doi.org/10.3390/appliedmath4030043

**Chicago/Turabian Style**

Stoll, Elizabeth A.
2024. "The Mechanics Underpinning Non-Deterministic Computation in Cortical Neural Networks" *AppliedMath* 4, no. 3: 806-827.
https://doi.org/10.3390/appliedmath4030043