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Dynamical Lee-Yang zeros for continuous-time and discrete-time stochastic processes.

Hiroki Yoshida¹, Kazutaka Takahashi²

¹Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan.

Physical Review. E

|March 16, 2022

Summary

Dynamical Lee-Yang zeros characterize classical stochastic processes and current distributions in master equations. Time discretization yields continuous zeros, while periodic driving splits them, revealing geometric current properties.

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Area of Science:

Statistical Physics
Non-equilibrium Thermodynamics

Background:

Classical stochastic processes are fundamental in physics.
Understanding non-equilibrium systems requires advanced analytical tools.

Purpose of the Study:

To introduce dynamical Lee-Yang zeros for analyzing classical stochastic processes.
To investigate the behavior of current distributions in driven systems.

Main Methods:

Utilizing the two-state classical master equation.
Employing dynamical Lee-Yang zeros to characterize the cumulant generating function.
Discretizing time and applying Floquet-Magnus expansion.

Main Results:

A factorized form of the cumulant generating function was derived.
Continuous and split distributions of dynamical Lee-Yang zeros were observed.
Geometric properties of current were analyzed and compared to adiabatic approximations.

Conclusions:

Dynamical Lee-Yang zeros provide a powerful method for studying stochastic processes.
Time-dependent driving significantly alters the distribution of these zeros.
The approach offers insights into non-equilibrium dynamics and current fluctuations.