Entropic Time Psychophysics Deformed Neural Dynamics

---
name: entropic-time-psychophysics-deformed-neural-dynamics
description: Unified physical theory linking entropy production, subjective time perception, and deformed neural dynamics. Derives conformable time operators from thermodynamic principles and predicts psychedelic time dilation and cognitive aging effects.
tags: [time-perception, thermodynamics, neural-dynamics, psychophysics, tsallis-entropy, conformable-calculus, psychedelic-states, cognitive-aging]
arxiv_id: "2606.29427v1"
date: 2026-06-28
authors: ["Unknown"]
categories: ["q-bio.NC", "physics.bio-ph"]
---

# Entropic Time, Psychophysics, and Deformed Neural Dynamics

## Core Insight

Human subjective time perception does NOT track geometric coordinate time t, but emerges from **local metric mutation driven by macroscopic physical entropy production**. This unified theory eliminates independent phenomenological fitting constants by establishing the "Nonextensive Troika" — a closed algebraic triplet linking phase-space fractal dimension D, conformable derivative order α, and Tsallis nonextensive parameter q.

## Key Contributions

### 1. Nonextensive Troika (D, α, q)
- **D**: Phase-space fractal dimension
- **α**: Conformable derivative order  
- **q**: Tsallis nonextensive parameter
- These three parameters are **mutually dependent** — no independent fitting needed
- Structural closure eliminates phenomenological freedom

### 2. Conformable Time Operator Derivation
- Local time metric inherently scales as **t^α**
- Conformable derivative emerges as **necessary kinetic consequence** of entropy production
- Not an ad hoc mathematical tool — derived from first principles

### 3. q-Index from Tsallis Entropy
- Derive q from equiprobable monofractal Tsallis entropy: S_q
- Links information theory to thermodynamic irreversibility
- Provides microscopic foundation for nonextensive statistics

### 4. Deformed Leaky Integrate-and-Fire Framework
- Anomalous neural dissipative transport unified within deformed LIF model
- Time-dependent membrane dynamics follow conformable calculus
- Captures non-Markovian neural processing

### 5. Psychophysical Predictions
- **Psychedelic states (REBUS model)**: Predicts time dilation from increased entropy production
- **Cognitive aging**: Predicts temporal compression from reduced entropy production
- Analytically derives macroscopic response transitions

## Methodology

### Theoretical Framework
1. Start with entropy production rate in neural tissue
2. Derive conformable time derivative from thermodynamic irreversibility
3. Establish D-α-q algebraic constraints
4. Formulate deformed LIF equations with conformable derivatives
5. Solve for psychophysical response functions

### Key Equations
- Conformable derivative: D^α_t f(t) = lim_{ε→0} [f(t + εt^{1-α}) - f(t)] / ε
- Tsallis entropy: S_q = k(1 - Σp_i^q) / (q-1)
- Time scaling: τ_local = t^α

### Predictions
- Time dilation factor ∝ entropy production rate
- Aging compression ∝ reduced metabolic entropy
- Psychedelic effects ∝ REBUS model entropy increase

## Implications

### For Neuroscience
- Time perception is thermodynamic, not computational
- Neural dynamics are fundamentally non-Markovian
- Fractal dimension constrains temporal processing

### For Physics
- Bridges thermodynamics and subjective experience
- Provides physical basis for "psychological time"
- Unifies disparate psychophysical phenomena

### For Clinical Applications
- Quantitative predictions for psychedelic therapy
- Biomarkers for cognitive aging
- Objective measures of temporal processing disorders

## Activation Triggers

time perception, subjective time, thermodynamics, entropy production, conformable calculus, Tsallis entropy, nonextensive statistics, psychedelic states, REBUS model, cognitive aging, temporal dilation, fractal dimension, deformed neural dynamics