The average distance that particles can travel between their collisions according to the kinetic theory of heat is called the mean free path. Likewise, the limited mobility of free electrons in crystal lattices is measured using the physical concept of a mean free path. Subsequently, if the mean free path becomes a radius of a spherically controlled volume then the resulting sphere defines a mean free volume. As the average kinetic energy of the colliding particles increases the size of the mean free volume decreases, suggesting that kinetic energy of collision is inversely proportional to the cube of the mean free path or inversely to the mean free volume. Expressed mathematically, the product of kinetic energy and volume gives a new physical constant. It is up to experiments to determine this constant for various types of colliding particles.

Applying this concept to the thermonuclear (hot) fusion of deuterons, it can be determined that the mean free volume is physically related to the size of the deuteron. This size is also a physical constant determined by experiments. At the outset if two energetic deuterons are trapped inside a larger controlled volume then as its size decreases the expected probability that these two deuterons will be fused increases. Nonetheless, the mean free volume of deuterons is the difference in volume specified by their sizes minus the expansive kinetic volume of collision. This formulation is applicable to hot fusion as well as to cold fusion. For the latter, the kinetic volume of collision approaches zero such that the mean free volume becomes the funnel-shape controlled volume of the specific volume contractor for cold fusion, and equivalently the mean free path becomes the gradually decreasing crystal lattice spacing as the deuterons pass through. The geometry need not be a sphere as long as the genus of its topology is zero. Generalized topologies of varying values for the genus will be discussed elsewhere.