Comment on "Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven...

Area of Science:

• Statistical Mechanics
• Complex Systems
• Non-equilibrium Physics

Background:

• Dynamical large deviations analyze fluctuations in non-equilibrium systems.
• Buča et al. interpreted a singularity in a double limit as a first-order phase transition in a cellular automaton.
• This interpretation aligns with treating time as a spatial coordinate in thermodynamic systems.

Purpose of the Study:

• To critically examine the interpretation of dynamical large deviations in Buča et al.'s cellular automaton model.
• To investigate the consistency of the double-limit procedure with the model's fundamental properties.
• To propose an alternative limiting procedure and analyze its implications for phase transitions.

Main Methods:

• Analysis of the large-deviation function derived from a specific double limit (time then space).
• Comparison of the derived large-deviation function with the model's inherent characteristics.
• Development and application of a modified limiting procedure.

Main Results:

• The large-deviation function from the double limit is inconsistent with the model's basic features.
• A modified limiting procedure yields a nonsingular large-deviation function.
• The results from the modified limit do not support the existence of coexisting dynamical phases.

Conclusions:

• The interpretation of a first-order phase transition and coexisting dynamical phases in Buča et al. is questionable.
• A revised limiting approach provides a more consistent description of the model's dynamics.
• The study suggests that the observed singularity may not represent a true phase transition in the thermodynamic sense.