  Acceleration of relaxation toward a fixed stationary distribution via
violation of detailed balance was reported in the context of a Markov chain
Monte Carlo method recently. Inspired by this result, systematic methods to
violate detailed balance in Langevin dynamics were formulated by using
exponential and rotational nonconservative forces. In the present paper, we
accentuate that such specific nonconservative forces relate to the large
deviation of total heat in an equilibrium state. The response to these
nonconservative forces can be described by the intrinsic fluctuation of the
total heat in the equilibrium state. Consequently, the fluctuation-dissipation
relation for nonequilibrium steady states is derived without recourse to a
linear response approximation.
