Pressure in an exactly solvable model of active fluid

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Non-equilibrium Systems

Background:

• Active particles exhibit self-propulsion and persistent motion, crucial for biological and synthetic systems.
• Stochastic models like Active Brownian particle (ABP), Gaussian colored noise (GCN), and unified colored noise approximation (UCNA) are used to describe their behavior.
• Calculating pressure in these non-equilibrium systems presents unique challenges compared to equilibrium systems.

Purpose of the Study:

• To investigate and compare the steady-state pressure in three key stochastic models of active particles.
• To derive a general formula connecting the pressures of the GCN and UCNA models.
• To explore the universality of pressure calculations across different models and methods.

Main Methods:

• Analysis of steady-state pressure in ABP, GCN, and UCNA models.
• Application of the virial route for pressure calculation, which is generally applicable to these models.
• Derivation of a formula establishing a correspondence between GCN and UCNA pressures for generic potentials.
• Specialization to a system of elastic dumbbells in a parabolic well for explicit calculations.

Main Results:

• The pressure in the UCNA model can be calculated using thermodynamic, virial, and mechanical methods, yielding consistent results.
• The GCN model's pressure, when calculated using three methods, is identical to the UCNA pressure.
• A universal pressure behavior is observed across the models, particularly through the virial route.
• The ABP model's virial pressure precisely matches the results from the UCNA and GCN models.

Conclusions:

• The study demonstrates a universal behavior in the steady-state pressure of active particle models.
• A direct correspondence is established between GCN and UCNA pressures, simplifying analysis.
• The findings suggest that different stochastic models and calculation methods can yield consistent pressure values for active systems.