▁is ▁extern ally ▁driven ▁from ▁zero ▁to ▁one , ▁according ▁to ▁an ▁arbitrary ▁time ▁sched uling , ▁will ▁be ▁referred ▁as ▁ ▁forward ▁transformation ▁, ▁while ▁the ▁time ▁revers al ▁path ▁will ▁be ▁indicated ▁as ▁ ▁back ward ▁transformation . ▁Given ▁these ▁definitions , ▁the ▁C FT ▁sets ▁a ▁relation ▁between ▁the ▁following ▁five ▁quantities : ▁ ▁, ▁▁ ▁i . e . ▁▁ ▁the ▁joint ▁probability ▁of ▁taking ▁a ▁micro state ▁ ▁from ▁the ▁canonical ▁ensemble ▁corresponding ▁to ▁ ▁and ▁of ▁performing ▁the ▁forward ▁transformation ▁to ▁the ▁micro state ▁ ▁corresponding ▁to ▁; ▁ ▁, ▁ ▁i . e . ▁ ▁the ▁joint ▁probability ▁of ▁taking ▁the ▁micro state ▁ ▁from ▁the ▁canonical ▁ensemble ▁corresponding ▁to ▁ ▁and ▁of ▁performing ▁the ▁back ward ▁transformation ▁to ▁the ▁micro state ▁ ▁corresponding ▁to ▁; ▁ ▁, ▁where ▁ ▁is ▁the ▁Bol tz mann ▁constant ▁and ▁ ▁the ▁temperature ▁of ▁the ▁res er voir ; ▁ ▁, ▁ ▁i . e . ▁ ▁the ▁work ▁done ▁on ▁the ▁system ▁during ▁the ▁forward ▁transformation ▁( from ▁ ▁to ▁); ▁ ▁, ▁ ▁i . e . ▁ ▁the ▁Hel m hol tz ▁free ▁energy ▁difference ▁between ▁the ▁state ▁ ▁and ▁, ▁represented ▁by ▁the ▁canonical ▁distribution ▁of ▁micro states ▁having ▁ ▁and ▁, ▁respectively . ▁ ▁The ▁C FT ▁equation ▁reads ▁as ▁follows : ▁▁▁▁ ▁In ▁the ▁previous ▁equation ▁the ▁difference ▁ ▁corresponds ▁to ▁the ▁work ▁diss ip ated ▁in ▁the ▁forward ▁transformation , ▁. ▁The ▁prob abilities ▁ ▁and ▁▁ ▁become ▁identical ▁when ▁the ▁transformation