The molecular dynamics method is applied to theLa2−xSrxCuO4system to prove that canonicity conditions are violated in the case of a large contribution of anharmonism. This can lead to the formation of “hot” regions∼0.5 nmin the vicinity of Sr impurity atoms with an average kinetic energy two or three orders of magnitude higher than in the matrix even at low temperatures. The matrix is “effectively” cooled and can basically carry superconducting current due to percolation for any electron pairing mechanism. The velocity distribution is described by not one but at least two Maxwell functions. The fcc lattice of Ni near the phase-transition point also acquires “hot” spots which are not, however, localized in space, but migrate (with a lifetime∼10−12 s)and have a much smaller difference in kinetic energies (by a factor of 1.5–2.0). At low temperatures, canonicity conditions are always satisfied. ©1998 American Institute of Physics.