Properties of the dissipation functions for passive and active systems

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Non-equilibrium Physics

Background:

• The fluctuation theorem relates the probability distributions of system trajectories and their time-reversed counterparts.
• Understanding dissipation is crucial for analyzing non-equilibrium processes.

Purpose of the Study:

• Derive expressions for the dissipation function in both passive and active systems.
• Investigate the properties of the dissipation function for passive systems.
• Verify the fluctuation theorem numerically for a one-dimensional passive system.
• Relate the dissipation function to entropy production in active systems.

Main Methods:

• Utilized generic Langevin equations to model system dynamics.
• Defined the dissipation function based on trajectory probabilities and their time-reversals.
• Analyzed the dependence of the dissipation function on system variables and parameters.
• Performed numerical simulations for a one-dimensional system.
• Defined work done by active forces for active systems.

Main Results:

• For passive systems, the dissipation function depends solely on initial and final states, independent of the trajectory itself.
• The derived dissipation function for passive systems is independent of reactive and dissipative coupling coefficients.
• Numerical verification confirmed the fluctuation theorem for the obtained dissipation function in a 1D passive system.
• For active systems, the average rate of change of the dissipation function equals the average entropy production rate.

Conclusions:

• The derived dissipation function offers a simplified approach for analyzing passive systems.
• The findings provide a theoretical framework for understanding entropy production in both passive and active non-equilibrium systems.
• This work contributes to the broader understanding of statistical mechanics in non-equilibrium conditions.