|A rendition of extensive vs intensive variables explained via rabbits, drawn by Karen Thurber, from Daniel Schroeder's Thermal Physics (2000), according to which temperature, pressure, chemical potential, and density are "intensive variables", because they do not change with amount, whereas volume, particle count, entropy, enthalpy, free energy, and mass are "extensive" variables, because they change with amount. |
Small systems | Single particle systems
Shown adjacent is American physicist Daniel Schroeder's rendition of extensive and intensive variables in respect to a one-rabbit system as compared to a two-rabbit system, according to which volume V, internal energy U, and entropy S are said to double in going from the former to the latter, whereas pressure P and temperature T stay the same.
Schroeder’s single rabbit model, to note, has issues with it, in particular being that in the range of single particle thermodynamics or single molecule thermodynamics (each rabbit considered as an animate molecule, e.g. fish molecule), the issue of what becomes of "extensity" or "intensity" of thermodynamic variables, in the small system thermodynamics range, becomes a subject of discussion and further investigation; one point of view of which, as advocated by American chemical engineering thermodynamicist Ali Mansoori, being that the roles are reversed.  More mathematical thermodynamics investigation is needed in this area (particularly in the work of Leonhard Euler, possibly via modification to the Euler reciprocity relation).
1. Schroeder, Daniel V. (2000). An Introduction to Thermal Physics (one rabbit, two rabbit diagram, pg. 163). Addison Wesley Longman.
2. Mohazzabri, Pirooz, and Mansoori, Ali G. (2005). “Nonextensivity and Nonintensivity in Nanosystems: A Molecular Dynamics Simulation” (abs), Journal of Computational and Theoretical Nanoscience, 2(1): 138-47(10).
● Extensive and intensive properties – Wikipedia.