In 1939 Nazi Germany debuted the “lightning war,” or blitzkrieg, in Poland. This deadly military offensive involved mounting a burst of firepower-heavy attacks to cause confusion and break through an enemy's lines unexpectedly. Nearly 80 years later Russian physicists have found they can model this surprise tactic with a scientific law: the kinetic theory of gases.

The parallels are obvious enough, with some creative thought. Both armies and gases have densities—troops per square kilometer or atoms per cubic meter. Basic units also have measurable cross sections that define territorial coverage—for troops, average weapon range, and for atoms of gas, electron orbital reach. And for both entities, when cross sections overlap, confrontations occur. Further, in the case of a blitzkrieg, defenders' dispersion can be seen as resembling the widely separated atoms of a gas.

Thus, physicists Vladimir Aristov and Oleg Ilyin of the Russian Academy of Sciences took historical military data about the German and Polish forces in World War II—the number of soldiers, tanks, aircraft and artillery, as well as the initial invasion speed of motorized vehicles—and replaced each unit with gas molecules in a mathematical model based on kinetic theory. Atoms or molecules of gas conforming to this theory dart around randomly and collide with one another frequently, but order can be imposed by, for example, forcing the gas to flow through a pipe or nozzle. In Aristov and Ilyin's model, the German army was a fast-moving, concentrated stream of gas atoms that rapidly penetrated the widely spaced gas atoms that represented the Polish army.

According to the model's calculations, which account for slowing speeds from collisions, the Germans should have moved 50 kilometers a day—precisely their actual pace during the seven-day, 350-kilometer trek to Warsaw. The researchers also ran calculations for the blitzkriegs of France in 1940 and of the Soviet Union in 1941 and found that the model's predictions matched the historical front movements in those cases, too.* The analogy broke down, however, when the initial surprise attack ended, and defending troops of atoms started to “fight” more effectively. The research was published in April in the journal Physical Review E.

Attempts to explain sociohistorical phenomena with physics abound. For decades scientists have modeled events such as the spread of the Black Death in the 14th century with slow diffusion models, which describe processes such as the random drift of a drop of ink in a glass of water. Kinetic theory is best applied to more rapid, direct processes—such as a swift invasion. Ilyin says that their model could be used to predict the rates of future war-front advances but only if the opposing sides abide by conventional tactics—unlikely these days given the availability of nuclear weapons and unmanned drones.

*Editor's Note (9/3/15): This sentence from the print article was edited after it was posted online to correct an error. The original incorrectly stated that Germany attacked Stalingrad in 1941; the battle for that city occurred in 1942.