Brownian motion with stochastic energy renewals

Area of Science:

• Statistical Mechanics
• Non-Equilibrium Thermodynamics
• Soft Matter Physics

Background:

• Brownian motion describes particle movement due to random collisions.
• Standard models often assume equilibrium conditions or simple driving forces.
• Understanding non-equilibrium systems is crucial for complex phenomena.

Purpose of the Study:

• Investigate the effects of intermittent kinetic energy renewals on Brownian particles.
• Characterize the resulting non-equilibrium statistical properties and dynamics.
• Quantify the system's deviation from thermodynamic equilibrium.

Main Methods:

• Modeling Brownian particles with stochastic kinetic energy renewals.
• Analysis of underdamped Langevin dynamics between energy injection events.
• Derivation of modified fluctuation-response relations and analysis of dissipation.

Main Results:

• Discovery of non-Boltzmannian energy distributions with a tunable shape transition.
• Observation of dynamics mimicking run-and-tumble motion at high renewal rates.
• Identification of non-monotonic effective diffusion coefficients and absence of a consistent effective temperature.

Conclusions:

• Intermittent energy injections drive systems significantly out of equilibrium.
• The system's behavior depends critically on the interplay between relaxation and renewal timescales.
• A dimensionless coefficient quantifies the thermodynamic cost of sustained diffusion in these non-equilibrium systems.