Entropy Governed by the Absorbing State of Directed Percolation

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.

8(=4+4)pages, 13(=5+6) figures

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Cited by in corpus (7)

• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Directed percolation in non-unitary quantum cellular automata
• Quantum and classical temporal correlations in $(1+1)D$ Quantum Cellular Automata
• Principal component analysis of absorbing state phase transitions
• Universal Scaling Laws of Absorbing Phase Transitions in Artificial Deep Neural Networks
• Exact epidemic models from a tensor product formulation
• Universal spectrum structure at nonequilibrium critical points in the (1+1)-dimensional directed percolation