
In 1905, Albert Einstein explained Brownian motion in terms of molecular collisions between the visible particles with the invisible solvent molecules, whereby owing to constant and random bombardment, sometimes a particle is pushed one way, sometimes another, smaller particles move more than larger ones, and motions increase with increasing temperature.

In 1905, Albert Einstein explained Brownian motion in terms of molecular collisions between the visible particles with the invisible solvent molecules, whereby owing to constant and random bombardment, sometimes a particle is pushed one way, sometimes another, smaller particles move more than larger ones, and motions increase with increasing temperature.

In hmolscience, active Brownian agent, or Brownian agent, is agent conceived as a point-like particle that has active Brownian motion, the term “active” meaning the ability of an individual unit to move actively by gaining kinetic energy from the environment, active particles or agents assumed to have an internal propulsion mechanism (motor) and may use energy from an external source and transform it under non-equilibrium conditions into directed accelerated motion. [1]

Etymology
The term “active Brownian motion” was introduced in 1995 by German theoretical physicists Lutz Schimansky-Geier, Michaela Mieth, Helge Rose, and Horst Malchow as follows: [2]

“We call Brownian particles with the ability to generate a field active Brownian particles if the produced field self-consistently determines the motion of the particles or defines their rates of chemical reactions.”

Since this introduction, the term seems to have taken on an expanded or alternative meaning, depending. Werner Ebeling, Lutz Schimansky-Geier, et al, in 2012 gave the following history: [1]

“The concept of 'active Brownian particles' introduced more than a decade ago. The term was first introduced by [Schimansky-Geier, et al] [2], referring to Brownian particles with the ability to generate a field, which in turn can influence their motion. In the following Ebeling, Schweitzer and others used this term in the context of self-propelled particles far from equilibrium. In general we will refer to “active Brownian particles” in the latter context as Brownian particles performing active motion, which may be accounted for by an internal energy depot and or a (nonlinear) velocity-dependent friction function.”

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References
1. Romanczuk, Pawel Bar, M., Ebeling, Werner, Lindner, B., and Schimansky-Geier, Lutz. (2012). Active Brownian Particles: From Individual to Collective Stochastic Dynamics; Dedicated to the Late Frank Edward Moss (1934 - 2011) Volume 202 of The European physical journal special topics (abs) (pdf). EDP sciences.
2. Schimansky-Geier, Lutz, Mieth, Michaela, Rose Helge, and Malchow, Horst. (1995). “Structure Formation by Active Brownian Particles” (abs), Physics Letters A, 2-07:140-46.

Further reading
● Schweitzer, Frank. (1997). “Active Brownian Particles: Artificial Agents in Physics”, in Stochastic Dynamics, Lecture Notes in Physics (editors: Lutz Schimansky-Geier and T. Poschel) (pgs. 358-71), Volume 484. Springer.
● Erdmann, Udo, Ebeling, Werner, Schimansky-Geier, Lutz, and Schweitzer, Frank. (2000). “Brownian Particles Far From Equilibrium” (pdf), The European Physical Journal B-Condensed Matter and Complexity, 15(1):105-13.
● Ebeling, Werner, Schweitzer, Frank, and Tilch, Benno. (1999). “Active Brownian Particles with Energy Depots Modeling Animal Mobility”, Biosystems, 4(1):17-29.
● Schweitzer, Frank. (2003). Brownian Agents and Active Particles: Collective Dynamics in the Natural Sciences. Springer, 2007.