Thermodynamic and quantum thermodynamic answers to Einstein's concerns   about Brownian movement
  On the occasion of the 100th anniversary of the beginning of the revolutionary contributions to physics by Einstein, I am happy to respond to a problem posed by him in 1905. He said: In this paper it will be shown that according to the molecular-kinetic theory of heat, bodies of microscopically-visible size suspended in a liquid will perform movements of such magnitude that they can be easily observed in a microscope, on account of the molecular motions of heat....that is, Brownian molecular motion. In this article I provide incontrovertible evidence against molecular-kinetic conception of heat, and a regularization of the Brownian movement that differs from all the statistical procedures and/or analyses that exist in the archival literature to date. The regularization is based on either of two distinct but intimately interrelated revolutionary conceptions of thermodynamics, one is purely thermodynamic and the other is quantum mechanical. 
Elias P. Gyftopoulos