Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement

Brownian movement has a history of more than two centuries. Studies that appeared in the scientific archival literature in the period until 1920 are listed by Einstein [1]. Articles that were written until 1970 are presented in Refs. [2] and [3]. Three-dimensional Brownian motors are discussed in [4], and Brownian movement of E. coli in [5]. All these studies and articles are based on a variety of statistical interpretations of thermodynamics, and on the conception of the molecular-kinetic theory of heat. Maxwell [6] conceived his omniscient and omnipotent demon who can contradict a circularly postulated second law of thermodynamics, and concludes ... “In dealing with masses of matter, while we do not perceive the individual molecules, we are compelled to adopt what I have described as the statistical method of calculation, and to abandon the strict dynamical method in which we follow every molecule by the calculus”.