  The no-pumping theorem refers to a Markov system that holds the detailed
balance, but is subject to a time-periodic external field. It states that the
time-averaged probability currents nullify in the steady periodic (Floquet)
state, provided that the Markov system holds the Arrhenius transition rates.
This makes an analogy between features of steady periodic and equilibrium
states, because in the latter situation all probability currents vanish
explicitly. However, the assumption on the Arrhenius rates is fairly specific,
and it need not be met in applications. Here a new mechanism is identified for
the no-pumping theorem, which holds for symmetric time-periodic external fields
and the so called destination rates. These rates are the ones that lead to the
locally equilibrium form of the master equation, where dissipative effects are
proportional to the difference between the actual probability and the
equilibrium (Gibbsian) one. The mechanism also leads to an approximate
no-pumping theorem for the Fokker-Planck rates that relate to the
discrete-space Fokker-Planck equation.
