Exact pretransition effects in kinetically constrained circuits: Dynamical fluctuations in the Floquet-East model

Area of Science:

• Statistical Mechanics
• Complex Systems Dynamics
• Computational Physics

Background:

• The kinetically constrained East model describes systems with restricted dynamics.
• Understanding emergent phenomena like the hydrophobic effect in simplified models is crucial.
• Classical circuits offer a tractable framework for studying complex dynamics.

Purpose of the Study:

• To investigate the dynamics of a discrete-time classical circuit analogous to the East model.
• To explore pre-transition behaviors and their connection to physical phenomena like the hydrophobic effect.
• To analyze phase transitions and scaling properties in this classical dynamical system.

Main Methods:

• Development of a classical circuit model (Floquet-East model).
• Exact mathematical proofs for the deterministic version of the model.
• Analysis of probability distributions in space-time regions.
• Investigation of dynamical large deviations and phase transitions.

Main Results:

• The Floquet-East model exhibits pre-transition behavior dynamically equivalent to the hydrophobic effect.
• A change in scaling with system size was proven for inactive space-time regions.
• A first-order phase transition was identified in dynamical large deviations.
• Optimal geometries for local phase separation and a dynamical analog of hydrophobic collapse were established.

Conclusions:

• Classical circuit models can effectively mimic complex physical phenomena such as the hydrophobic effect.
• The study provides exact mathematical insights into phase transitions and scaling in constrained dynamical systems.
• The Floquet-East model serves as a valuable theoretical tool for understanding emergent behaviors in statistical physics.