Algebraic topology and the quantization of fluctuating currents

TL;DR

This paper introduces an algebraic topology approach to analyze stochastic currents in graphs, demonstrating quantization of current generation in certain limits, offering a novel perspective in statistical mechanics.

Contribution

It presents a new algebraic topology framework for studying fluctuating currents and proves quantization occurs in specific physical limits.

Findings

Quantization of current generation in low temperature and adiabatic limits

Algebraic topology provides a new method for analyzing stochastic systems

Demonstrates the applicability of topological methods in statistical mechanics

Abstract

We give a new approach to the study of statistical mechanical systems: algebraic topology is used to investigate the statistical distributions of stochastic currents generated in graphs. In the adiabatic and low temperature limits we will demonstrate that quantization of current generation occurs.