  We introduce the "leaking elastic capacitor" (LEC) model, a nonconservative
dynamical system that combines simple electrical and mechanical degrees of
freedom. We show that an LEC connected to an external voltage source can be
destabilized (Hopf bifurcation) due to positive feedback between the mechanical
separation of the plates and their electrical charging. Numerical simulation
finds regimes in which the LEC exhibits a limit cycle (regular
self-oscillation) or strange attractors (chaos). The LEC acts as an autonomous
engine, cyclically performing work at the expense of the constant voltage
source. We show that this mechanical work can be used to pump current,
generating an electromotive force without any time-varying magnetic flux and in
a thermodynamically irreversible way. We consider how this mechanism can
sustain electromechanical waves propagating along flexible plates. We argue
that the LEC model can offer a qualitatively new and more realistic description
of important properties of active systems with electrical double layers in
condensed-matter physics, chemistry, and biology.
