# Exploring Ohm’s Law: The Randomness of Determinism

## TL;DR

This paper introduces a visual model to help students understand Ohm’s law by linking electron movement in solids to energy and entropy concepts.

## Contribution

The study introduces a novel strategy for describing electron trajectory randomization and its connection to material structure and resistivity.

## Key findings

- Electron trajectories follow maximum trajectory entropy.
- Thermal entropy has a quadratic relationship with configurational entropy.
- Ohm’s law determinism is derived from statistical entropy.

## Abstract

Ohm’s law has become ubiquitous in numerous scientific and technical disciplines. Generally, the subject is introduced to students in secondary school as fundamental technical knowledge. The present study proposes a visual model to facilitate the comprehension of Ohm’s law in electron transport in solids to pre-university and university students. The objective is to facilitate students’ comprehension of the correlation between electron movement in solids, as depicted by a current, and the energy of the system, which is introduced by the electric field and the material’s structure. The approach’s originality lies in its novel strategy for describing electron trajectory randomization. This enables the establishment of a relationship between the material’s structure and its resistivity. Moreover, the description of electron transport and scattering processes is presented regarding different types of entropy. It shows that electrons follow the maximum trajectory entropy and that thermal entropy has a quadratic relationship with configurational entropy. The determinism of Ohm’s law is inferred from statistical entropy.