Testing the Equivalence between Spatial Averaging and Temporal Averaging in Highly Dilute Solutions

Area of Science:

• Statistical Physics
• Physical Chemistry
• Colloid Science

Background:

• Diffusion describes particle flux based on density gradients.
• Low particle densities challenge the definition of local gradients.
• Statistical physics resolves this using probabilistic descriptions and thermal equilibrium.

Purpose of the Study:

• To experimentally test the fundamental equivalence principle in statistical physics.
• To investigate diffusion dynamics at extremely low particle concentrations.
• To validate the probabilistic description of diffusion.

Main Methods:

• Studied the flux distribution of 20 nm polystyrene particles towards a micrometer-sized sink.
• Maintained particle concentration at approximately 1 particle per sink volume element.
• Utilized a novel experimental method to measure particle flux statistics.

Main Results:

• Measured flux density precisely matches the diffusion equation for an infinite system.
• Flux statistics exhibit a Poissonian distribution, consistent with Markovian random walks.
• Demonstrated that finite systems emulate infinite systems over extended durations.

Conclusions:

• Confirms the equivalence principle in diffusion dynamics, even at low densities.
• Validates the use of probabilistic flux density in diffusion models.
• Highlights the long-term emergent behavior of finite systems mirroring infinite ones.