Thermodynamic entropy production fluctuation in a two-dimensional shear flow model

Area of Science:

• Statistical Mechanics
• Non-equilibrium Thermodynamics
• Fluid Dynamics

Background:

• Investigating fluctuation relations is crucial for understanding non-equilibrium systems.
• Previous work established fluctuation relations for Gibbs ensemble entropy production.
• Hydrodynamic entropy production in driven systems requires further examination.

Purpose of the Study:

• To analyze momentum flux fluctuations in stationary shear flow under deterministic and stochastic conditions.
• To determine the applicability of fluctuation relations to hydrodynamic entropy production.
• To explore heat flux behavior in systems with stochastic boundaries at different temperatures.

Main Methods:

• Simulations of stationary shear flow using thermostated deterministic boundary conditions.
• Simulations of stationary shear flow using stochastic boundary conditions.
• Analysis of momentum and heat flux fluctuations across defined surfaces.

Main Results:

• In deterministic systems, fluctuation relations for hydrodynamic entropy production (momentum flux) were not observed.
• In stochastic systems, fluctuation relations held for total momentum flux but not for partial flux, indicating a modified relation.
• Similar deviations from standard fluctuation relations were found for heat flux in stochastic systems.

Conclusions:

• Standard fluctuation relations may not universally apply to hydrodynamic entropy production, especially for partial fluxes.
• Stochastic boundary conditions can lead to modified fluctuation relations for momentum and heat flux.
• Further theoretical and computational studies are needed to fully characterize fluctuation phenomena in non-equilibrium systems.