  Empirical diagnosis of stability has received considerable attention, mostly
focused on variance metrics for early warning signals of abrupt system change.
Despite this, the theoretical foundation and application has been limited to
relatively simple system changes such as bifurcating fixed points where
variability is extrinsic to the steady state. There is currently no foundation
and associated metric for empirically exploring stability in wide ranging
systems that contain variability in both internal steady state dynamics and in
response to external perturbations. Utilizing connections between stability,
dissipation, and phase space flow, we show that stability correlates with
temporal asymmetry in a measure of phase space flow contraction. Our method is
general as it reveals stability variation independent of assumptions about the
nature of system variability or attractor shape. After showing efficacy in a
variety of model systems, we apply our technique for measuring stability to
monthly returns of the S&P 500 index in the time periods surrounding the global
stock market crash of October 1987. Market stability is shown to be higher in
the several years preceding and subsequent to the 1987 market crash. We
anticipate our technique will have wide applicability in climate, ecological,
financial, and social systems where stability is a pressing concern.
