  We theoretically explore the Bochkov-Kuzovlev-Jarzynski-Crooks work theorems
in a finite system subject to external control, which is coupled to a heat
reservoir. We first elaborate the mechanical energy-balance between the system
and the surrounding reservoir and proceed to formulate the statistical
counterpart under the general nonequilibrium conditions. Consequently, a
consistency condition is derived, underpinning the nonequilibrium equalities,
both in the framework of the system-centric and nonautonomous Hamiltonian
pictures and its utility is examined in a few examples. Also, we elucidate that
the symmetric fluctuation associated with forward and backward manipulation of
the nonequilibrium work is contingent on time-reversal invariance of the
underlying mesoscopic dynamics.
