  The vacuum persistence can be written as the Bose-Einstein distribution in
spinor QED and as the Fermi-Dirac distribution in scalar QED exactly in a
constant electric field and approximately in time-varying electric fields. The
inverse temperature is determined by the period of charged particle in the
Euclidean time and the negative chemical potential by the ratio of the
worldline instanton to the inverse temperature. The negativity of chemical
potential is due to the vacuum instability under strong electric fields. The
inversion of spin statistics in the vacuum persistence is a consequence of the
Bogoliubov relations for fermions and bosons.
