Nonequilibrium Equalities in Absolutely Irreversible Processes
  We generalize nonequilibrium integral equalities to situations involving absolutely irreversible processes for which the forward-path probability vanishes and the entropy production diverges, rendering conventional integral fluctuation theorems inapplicable. We identify the mathematical origins of absolute irreversibility as the singularity of probability measure. We demonstrate the validity of the obtained equalities for several models. 
Y\^uto Murashita, Ken Funo, and Masahito Ueda
cond-mat.stat-mech