Paradoxical nonlinear response of a Brownian particle

We consider a Brownian particle in a meandering periodic potential when the ambient temperature is a periodically or stochastically varying function of time. Though far from equilibrium, the linear response of the particle to an external static force is exactly the same as in the equilibrium case, i.e., for constant temperature. Even more surprising is the nonlinear response: the particle slows down and then even starts to move in the direction opposite to the applied force.