# Ihara Zeta Entropy

## TL;DR

This paper introduces a novel entropy measure derived from the Ihara Zeta function, with applications in symbolic dynamics and billiard systems, supported by new inequalities related to the zeta function.

## Contribution

It proposes a new entropy based on the Ihara Zeta function and establishes inequalities, expanding tools for analyzing dynamical systems.

## Key findings

- Derived a new entropy measure from the Ihara Zeta function.
- Established inequalities involving the Ihara Zeta function values.
- Applied the entropy to symbolic dynamics and billiard systems.

## Abstract

In this article, we introduce an entropy based on the formal power series expansion of the Ihara Zeta function. We find a number of inequalities based on the values of the Ihara zeta function. These new entropies are applicable in symbolic dynamics and the dynamics of billiards.