The familiar analogy between the quantum time evolution of an isolated
system and the thermal equilibrium of an open system with a thermosta
t is considered as a signal of a profound thermodynamic-type aspect of
the physical time, suggesting small nonunitarity corrections to the c
onventional quantum theory. These imply, as their characteristic conse
quence, a tiny unitarity defect of S matrix. Another surprising conseq
uence is a slight time dependence of mass of any matter system localiz
ed close to an experimental device such as a running supercollider or
a big laser in action, where an intensive particle flow is produced. T
his suggests a described gedankenexperiment.