The dynamic behavior of compressible flows is governed by the dimensionless thermodynamic quantity , which is known as the fundamental derivative of gasdynamics and is defined as
where
*  is the speed of sound [m/s];
*  is the specific entropy per unit mass [J/(kg K)].
From a mathematical point of view, the fundamental derivative is a non-dimensional measure of the curvature of isentropes in the pressure-volume thermodynamic plane. From a physical point of view, the definition of  tells that the speed of sound increases with pressure in isentropic transformations for values of , while, by contrast, it decreases with pressure for .
Based on the value of , three gasdynamic regimes can be defined:
* ideal gasdynamic regime for ;
* non-ideal classical gasdynamic regime for ;
* non-classical gasdynamic regime for .