# The World as a Neural Network

## Abstract

**:**

## 1. Introduction

## 2. Neural Networks

## 3. Thermodynamics of Learning

**Second Law of Learning:**

**First Law of Learning:**

## 4. Entropic Mechanics

**Principle of Stationary Entropy Production:**

## 5. Quantum Mechanics

- (1)
- $-4D\frac{{\partial}^{2}}{\partial {q}_{k}^{2}}$, entropy production due to stochastic dynamics of ${q}_{k}$’s,
- (2)
- $\gamma \frac{{\partial}^{2}F}{\partial {q}_{k}^{2}}$, entropy production due to learning dynamics of ${q}_{k}$’s,
- (3)
- $\mu \frac{\partial F}{\partial t}$, free energy production due to dynamics of ${x}_{i}$’s,
- (4)
- $\mu \gamma {\left(\frac{\partial F}{\partial {q}_{k}}\right)}^{2}$, free energy production due to learning dynamics of ${q}_{k}$’s, and
- (5)
- $\mu V$, the (negative of) total time-averaged free energy production.

## 6. Hamiltonian Mechanics

## 7. Hidden Variables

## 8. Relativistic Strings

## 9. Emergent Gravity

## 10. Holography

## 11. Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

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Vanchurin V. The World as a Neural Network. *Entropy*. 2020; 22(11):1210.
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