  A simulation-based study of Kramers' escape problem in the bistable well of a
ferroelectric capacitor is presented. This problem deals with the escape of a
particle undergoing Brownian motion over an energy barrier. Using this
framework, and under the assumption of homogeneous polarisation switching
according to the Landau-Ginzburg-Devonshire (LGD) theory, we outline two
prospective device applications -- the possibility of observing true random
number generation (TRNG) and stochastic resonance (SR) in a ferroelectric
capacitor. Our simulation results for the former show that by adding white
noise and an appropriately tuned voltage pulse to a ferroelectric capacitor, it
is possible to facilitate probabilistic switching between its two stable
polarisation states. We predict that this could provide the theoretical
framework for practical implementations of TRNGs. In addition, we investigate
stochastic resonance in a ferroelectric capacitor using linear response theory.
We show that the addition of an optimal amount of noise to a weak periodic
signal, given as an input to this system, can enhance its detection.
