  Jarzynski's nonequilibrium work relation can be understood as the realization
of the (hidden) time-generator reciprocal symmetry satisfied for the
conditional probability function. To show this, we introduce the reciprocal
process where the classical probability theory is expressed with real wave
functions, and derive a mathematical relation using the symmetry. We further
discuss that the descriptions by the standard Markov process from an initial
equilibrium state are indistinguishable from those by the reciprocal process.
Then the Jarzynski relation is obtained from the mathematical relation for the
Markov processes described by the Fokker-Planck, Kramers and relativistic
Kramers equations.
