Reconstructing free-energy landscapes for nonequilibrium periodic potentials

Area of Science:

• Statistical physics
• Soft matter physics
• Computational physics

Background:

• Brownian motion describes random particle movement due to thermal fluctuations.
• Free-energy landscapes are crucial for understanding particle behavior in potentials.
• Periodic potentials and non-equilibrium conditions present significant analytical challenges.

Purpose of the Study:

• To develop a novel method for reconstructing free-energy landscapes.
• To analyze overdamped Brownian motion in tilted periodic potentials.
• To demonstrate the method's applicability across diverse potential landscapes and equilibrium regimes.

Main Methods:

• Utilizing the k-space form of the Smoluchowski equation to exploit system periodicity.
• Employing an iterative approach to determine the non-equilibrium tilt.
• Reconstructing landscapes for various example potentials, including those with deep and shallow wells.

Main Results:

• Successfully reconstructed free-energy landscapes for multiple example potentials.
• Demonstrated applicability to both deep and shallow wells.
• Validated the method for systems near-to- and far-from-equilibrium.
• Observed logarithmic convergence with the number of Fourier terms.

Conclusions:

• The k-space Smoluchowski equation method provides an effective way to reconstruct free-energy landscapes.
• The method is versatile, applicable to a wide range of periodic potentials and non-equilibrium conditions.
• This work offers a valuable tool for studying complex stochastic systems.