Geometrical interpretation of dynamical phase transitions in boundary-driven systems

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics

Background:

• Dynamical phase transitions occur at nonanalytic points in large deviation functions of current fluctuations.
• Boundary-driven systems are crucial for studying non-equilibrium phenomena.

Purpose of the Study:

• To identify dynamical phase transitions in boundary-driven systems using a novel geometrical approach.
• To propose an experimental method for observing these transitions.

Main Methods:

• Utilizing the macroscopic fluctuation theory to derive an effective potential Hamiltonian.
• Analyzing the geometrical structure of this effective potential to locate phase transitions.
• Comparing the new method with existing perturbative techniques.

Main Results:

• Identified new dynamical phase transitions not detectable by perturbative methods.
• Demonstrated that the geometrical structure of the effective potential Hamiltonian is key to identifying these transitions.
• Proposed an experimental scheme to observe analogs of dynamical phase transitions.

Conclusions:

• The geometrical analysis of effective potentials provides a powerful new tool for studying dynamical phase transitions.
• This method expands the scope of detectable phase transitions in non-equilibrium systems.
• The proposed experimental scheme offers a pathway for empirical validation.