  Bridging equilibrium and nonequilibrium statistical physics attracts
sustained interest. Hallmarks of nonequilibrium systems include a breakdown of
detailed balance, and an absence of a priori potential function corresponding
to the Boltzmann-Gibbs distribution, without which classical equilibrium
thermodynamical quantities could not be defined. Here, we construct dynamically
the potential function through decomposing the system into a dissipative part
and a conservative part, and develop a nonequilibrium theory by defining
thermodynamical quantities based on the potential function. Concepts for
equilibrium can thus be naturally extended to nonequilibrium steady state. We
elucidate this procedure explicitly in a class of time-dependent linear
diffusive systems without mathematical ambiguity. We further obtain the exact
work distribution for an arbitrary control parameter, and work equalities
connecting nonequilibrium steady states. Our results provide a direct
generalization on Jarzynski equality and Crooks fluctuation theorem to systems
without detailed balance.
