Numerical study of the steady state fluctuation relations far from equilibrium

Area of Science:

• Statistical Mechanics
• Dynamical Systems Theory
• Non-equilibrium Thermodynamics

Background:

• Fluctuation relations provide insights into non-equilibrium statistical mechanics.
• The Evans and Searles (Omega-FR) and Gallavotti and Cohen (Lambda-FR) relations are key theoretical frameworks.
• Lyapunov exponents characterize the stability and dynamics of chaotic systems.

Purpose of the Study:

• To numerically test the validity of the Omega-FR and Lambda-FR near and far from equilibrium.
• To investigate a conjecture proposing a correction to the Lambda-FR under specific conditions of Lyapunov exponents.
• To analyze the behavior of these fluctuation relations as a function of external driving field strength.

Main Methods:

• A thermostatted dynamical model with five degrees of freedom was employed.
• Numerical simulations were conducted both near and far from thermodynamic equilibrium.
• Lyapunov exponents were calculated to characterize the system's dynamics.

Main Results:

• The Omega-FR was consistently verified by simulation data across different equilibrium conditions.
• The uncorrected Lambda-FR showed increasing accuracy with increasing external field strength.
• No evidence was found to support the conjecture requiring a correction to the Lambda-FR under the specified conditions.

Conclusions:

• The Omega-FR is robustly supported by the numerical model.
• The conjecture regarding a corrected Lambda-FR is not supported by the empirical data.
• The observed accuracy of the uncorrected Lambda-FR at higher fields is attributed to its approximation of the Omega-FR.