# Entropy Governed by the Absorbing State of Directed Percolation

## TL;DR

This paper explores the entropy behavior in directed percolation, revealing universal relaxation at the phase transition and a new singularity in the active phase linked to the absorbing state, using tensor network methods.

## Contribution

It uncovers a new singularity in the Renyi entropy away from the critical point and links the absorbing state to entropy dynamics in directed percolation.

## Key findings

- Universal relaxation of Renyi entropy at the transition point
- Discovery of a new entropy singularity in the active phase
- Entanglement entropy behavior linked to the absorbing state

## Abstract

We investigate the informational aspect of (1+1)-dimensional directed percolation, a canonical model of a nonequilibrium continuous transition to a phase dominated by a single special state called the "absorbing" state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of directed percolation. We find a universal relaxation of Renyi entropy at the absorbing phase transition point as well as a new singularity in the active phase, slightly but distinctly away from the absorbing transition point. At the new singular point, the second-order Renyi entropy has a clear cusp. There we also detect a singular behavior of "entanglement entropy," defined by regarding the probability distribution as a wave function. The entanglement entropy vanishes below the singular point and stays finite above. We confirm that the absorbing state, though its occurrence is exponentially rare in the active phase, is responsible for these phenomena. This interpretation provides us with a unified understanding of time evolution of the Renyi entropy at the critical point as well as in the active phase.