Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment

We study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k B T , which is the "quantum" of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar in its structure. The subdiffusion that emerges in such a high-dimensional, fractal environment leads to a Fokker-Planck Equation with a fractional time derivative. We set up such a so-called fractional Fokker-Planck Equation for the aggregation into granules. From that Fokker-Planck Equation, we derive an expression for the entropy production of a growing granule.