A lattice gas of prime numbers and the Riemann Hypothesis

TL;DR

This paper models the non-trivial zeros of the Riemann zeta function using a one-dimensional lattice gas, showing that the critical point aligns with the Riemann Hypothesis, thus connecting physics concepts with a major mathematical conjecture.

Contribution

It introduces a novel physical model linking the zeros of the zeta function to a lattice gas system, providing a new perspective on the Riemann Hypothesis.

Findings

The real part of the zeros extremizes the grand potential.

The critical point of the model is at 1/2, supporting the Riemann Hypothesis.

The approach bridges physics and number theory in a new way.

Abstract

In recent years, there has been some interest in applying ideas and methods taken from Physics in order to approach several challenging mathematical problems, particularly the Riemann Hypothesis. Most of these kind of contributions are suggested by some quantum statistical physics problems or by questions originated in chaos theory. In this letter we show that the real part of the non-trivial zeros of the Riemann zeta function extremizes the grand potential corresponding to a simple model of one-dimensional classical lattice gas, the critical point being located at 1/2 as the Riemann Hypothesis claims.