  The literature on dynamical systems has, for the most part, considered
self-oscillators (i.e., systems capable of generating and maintaining a
periodic motion at the expense of an external energy source with no
corresponding periodicity) either as applications of the concepts of limit
cycle and Hopf bifurcation in the theory of differential equations, or else as
instability problems in feedback control systems. Here we outline a
complementary approach, based on physical considerations of work extraction and
thermodynamic irreversibility. We illustrate the power of this method with two
concrete examples: the mechanical instability of rotors that spin at
super-critical speeds, and the hydrodynamic Kelvin-Helmholtz instability of the
interface between fluid layers with different tangential velocities. Our
treatment clarifies the necessary role of frictional or viscous dissipation
(and therefore of irreversibility), while revealing an underlying unity to the
physics of many irreversible processes that generate mechanical work and an
autonomous temporal structure (periodic, quasi-periodic, or chaotic) in the
presence of an out-of-equilibrium background.
