A report is presented on some developments of the author's recent conj
ecture that a change of the overall particle number in a localized phy
sical process induces in its neighbourhood a small deformation of the
time run. This is a hypothetic quantum effect caused by a thermodynami
c-type mechanism not present in the Einsteinian classical theory of gr
avitation, but natural if the familiar analogy between the thermal equ
ilibrium and the unitary quantum time evolution is accepted as a physi
cally profound correspondence.