Evidence and quantification of memory effects in competitive first-passage events

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Splitting probabilities are crucial for understanding competitive events in random walk theory.
• Analytical characterization is limited for non-Markovian processes common in complex systems like polymer fluids.

Purpose of the Study:

• To introduce an analytical approach for calculating splitting probabilities in one-dimensional, isotropic, non-Markovian Gaussian processes with stationary increments.
• To investigate the factors controlling splitting probabilities in systems with memory.

Main Methods:

• Development of a novel analytical framework for non-Markovian processes.
• Analysis of out-of-equilibrium trajectories following first passage events.
• Experimental validation using a reaction scheme in viscoelastic fluids.

Main Results:

• The study provides a method to analytically determine splitting probabilities for complex, memory-dependent particle motion.
• Splitting probabilities are shown to be governed by post-first passage out-of-equilibrium dynamics.
• Experimental evidence confirms the theoretical predictions in a viscoelastic fluid system.

Conclusions:

• The new analytical approach extends the understanding of splitting probabilities to non-Markovian systems.
• The findings highlight the importance of trajectory dynamics in competitive event outcomes.
• This work paves the way for studying complex competitive events in various media.