POSSIBLE DEFORMATION OF TIME RUN INDUCED BY CHANGE OF PARTICLE NUMBER.2.

A discussion is continued on the author's recent conjecture that the o verall particle number, when it changes in a localized physical proces s, induces in its proximity a tiny deformation of the time run. In som e cases, the corresponding weak time-deformation field carl be emitted and also detected by matter sources. Sometimes, it can propagate free ly through the spacetime as ultraluminal waves. Though these hypotheti c waves cannot transport energy between matter sources, they can do it with a new thermodynamic-type quantity called here the energy width. This causes the quantum time evolution of matter sources to deviate sl ightly from the conventional unitary evolution.