Polarization of periodic degrees of freedom in response to cyclic transformations

When a classical fluctuating system in contact with a thermal bath undergoes a driven transformation in a finite time, a nonequilibrium distribution is created and an amount of energy is inevitably dissipated on average. It is known that the average dissipation and the extent of the out-of-equilibrium are mutually bounded. Here we elaborate the perspective of exploiting such a constraint to check the admissibility of the nonequilibrium distributions at a given amount of average dissipation. Namely, we focus on cyclic transformations and derive an upper bound for the statistical polarization that may be present, after the cycle, over an a priori unbiased periodic degree of freedom of the system. The finding is then applied to establish the maximum polarization that can be induced on the velocity of massive moieties in many-body molecular systems in response to generic cyclic transformations.