Work fluctuations for a Brownian particle driven by a correlated external random force

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Stochastic Processes

Background:

• Brownian motion describes the random movement of particles suspended in a fluid.
• External forces can influence Brownian particle dynamics, leading to complex behaviors.
• Understanding work fluctuations in driven systems is crucial for non-equilibrium thermodynamics.

Purpose of the Study:

• To analyze the work done by a correlated random force on a Brownian particle.
• To investigate the statistical properties of work fluctuations in the steady state.
• To explore the large deviation functions and symmetry properties of work performed.

Main Methods:

• Modeling the external force using the Ornstein-Uhlenbeck process.
• Calculating the probability density function of the performed work.
• Deriving and analyzing large deviation functions.
• Performing numerical simulations to validate analytical results.

Main Results:

• The complete asymptotic form of the probability density function for work was determined.
• Large deviation functions governing work fluctuations were calculated.
• Symmetry properties of these large deviation functions were discussed.
• Numerical simulations showed excellent agreement with the derived analytical results.

Conclusions:

• The study provides a comprehensive analysis of work fluctuations in a driven Brownian system.
• The findings offer insights into the statistical mechanics of non-equilibrium processes.
• The agreement between theory and simulation validates the model and methods used.