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Reply to "Comment on 'Exact large deviation statistics and trajectory phase transition of a deterministic boundary
Berislav Buča1,2, Juan P Garrahan3, Tomaž Prosen4
1Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Universitetsparken 5, 2100 Copenhagen, Denmark.
Physical Review. E
|October 18, 2023
Summary
This study confirms that singular behavior in large deviation (LD) statistics of rule 54 cellular automata indicates a dynamical phase transition, refuting contrary claims. Our exact computations support the standard interpretation of these findings.
Area of Science:
- Statistical physics
- Complex systems
Background:
- The study of large deviation (LD) statistics is crucial for understanding rare events in complex systems.
- Cellular automata, such as rule 54, provide a framework for modeling emergent behavior.
Purpose of the Study:
- To address a comment questioning the interpretation of previously computed exact large deviation statistics for the rule 54 cellular automaton.
- To reaffirm that the observed singular behavior in LD functions signifies a dynamical phase transition and phase coexistence.
Main Methods:
- Exact computation of large deviation statistics for a wide class of observables in the rule 54 cellular automaton.
- Analysis of the singular behavior of computed LD functions.
Main Results:
- The exact large deviation functions computed for rule 54 cellular automata exhibit singular behavior.
- This singularity is confirmed to be indicative of a dynamical phase transition and phase coexistence.
Conclusions:
- The standard interpretation of the exact large deviation statistics, indicating a dynamical phase transition, is upheld.
- The heuristic arguments presented in a prior comment are refuted based on rigorous mathematical analysis.
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