Multiplicity Distribution in the Multiperipheral Model and a One-Dimensional Gas

The multiplicity distribution at high energy in the multiperipheral model for the ${\phi }^3$ theory is shown to be identical to the grand canonical ensemble distribution of a particular one-dimensional gas with only repulsive forces, which can be decomposed into two-body, three-body, and other multibody forces. The specific form of these forces and the corresponding virial expansion of the gas system are discussed. An alternative systematic expansion method is developed which is different from the virial series but appears to be of a greater practical value for this particular class of physical problems.