Cost of Diffusion: Nonlinearity and Giant Fluctuations

Area of Science:

• Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Diffusive jump processes are fundamental in modeling various physical phenomena.
• Understanding cost functions in dynamic systems is crucial for predicting behavior.
• Existing models often lack the complexity to capture rich emergent behaviors.

Purpose of the Study:

• To introduce a novel diffusive jump model with a nonlinear cost function.
• To investigate the emergent behaviors and transitions within this model.
• To explore the applicability of the model to elastic systems.

Main Methods:

• Development of a simple diffusive jump model with a velocity-dependent cost.
• Analytical investigation of cost distributions for trajectories.
• Numerical simulations to corroborate analytical findings.
• Exploration of connections to elastic systems near depinning transitions.

Main Results:

• The model exhibits giant fluctuations in cost at a critical scaled distance.
• A 'freezing' transition in the large-deviation regime of cost distribution was observed.
• Analytical predictions were validated through numerical simulations.
• The model's relevance to elastic systems driven by random forces was demonstrated.

Conclusions:

• The nonlinear cost function in diffusive jump processes leads to complex and rich behaviors.
• The model provides a new framework for studying fluctuations and transitions in dynamic systems.
• The findings have implications for understanding phenomena like elastic depinning transitions.