Study on Single-molecule Biophysics and Biochemistry in Dilute Liquids and Live Cells without Immobilization or Significant Hydrodynamic Flow: The Thermodynamic Single-molecule Demon

Since mathematics provides a way to answer questions about the thermodynamic jitter in a clear, rational manner, with evidence to support it, mathematics is the reliable method necessary to get the best information on the movement of a single molecule / a single particle at the molecular scale in dilute liquids and live cells without immobilization or hydrodynamic flow. The Brownian movement (normal diffusive systems) and generally the thermodynamic jitter (anomalous diffusive systems) are ultimately the direct or indirect cause of every measurement signal at the molecular scale in diffraction limited and unlimited optical systems in dilute liquids and live cells without immobilization or hydrodynamic flow. For example, emitted photons are the epiphenomenon of the underlying process of thermodynamic jitter of single molecules / single particles at the molecular scale. The key question is: How far apart do two molecules / two particles have to be in the time domain so that the required degree of separation between the two individual molecules / the two individual particles can be quantified at the molecular scale in order to distinguish them as separate entities without immobilization or hydrodynamic flow? The Foldes-Papp's limits of the single-molecule time resolution in dilute liquids and live cells without immobilization or hydrodynamic flow are the exact answers. The diffusive process is complicated and not minimalist. A minimalist model has a third possibility, it may be right but irrelevant.