On the spherical prototype of a complex dissipative late-stage formation seen in terms of least action Vojta–Natanson principle

The spherical prototype of a crystalline and/or disorderly formation may help in understanding the final stages of many complex biomolecular arrangements. These stages are important for both naturally organized simple biosystems, such as protein (or, other amphiphilic) aggregates in vivo, as well as certain their artificial counterparts, mimicking either in vitro or in silico their structure–property principal relationship. For our particular one-seed based realization of a protein crystal/aggregate late-stage nucleus grown from nearby fluctuating environment, it turns out that the (osmotic-type) pressure could be, due to local inhomogeneities, and their dynamics shown up in the double layer tightly surrounding the growing object, still an appreciably detectable quantity. This is due to the fact that a special-type generalized thermodynamic (Vojta–Natanson) momentum, subjected to the nucleus’ surface, is manifested interchangeably, whereas the total energy of the solution in the double layer could not be such within the stationary regime explored. It is plausible since the double layer width, related to the object’s surface, contributes ultimately, while based on the so-defined momentum’s changes, to the pressure within this narrow flickering zone, while leaving the total energy fairly unchanged. From the hydrodynamic point of view, the system behaves quite trivially, since the circumventing flow should rather be of laminar, thus not-with-matter supplying, character.