Very high multiplicity hadron processes

The paper contains a description of a first attempt to understand the extremely inelastic high-energy hadron collisions, when the multiplicity of produced hadrons considerably exceeds its mean value. Problems with existing model predictions are discussed. The real-time finite-temperature S-matrix theory is built to have a possibility to find model-free predictions. This allows to take the statistical effects into consideration and build the phenomenology. The questions to experiment are formulated at the very end of the paper.