  The evolution of physical systems are often modeled by simple Markovian
processes. When settled into stationary states, the probability distributions
of such systems are time independent, by definition. However, they do not
necessarily fall within the framework of equilibrium statistical mechanics.
Instead, they may be non-equilibrium steady states (NESS). One distinguished
feature of NESS is the presence of time reversal asymmetry (TRA) and persistent
probability current loops. These loops lead naturally to the notion of
probability angular momenta, which play a role on the same footing as the noise
covariance in stochastic processes. Illustrating with simulations of simple
models and physical data, we present ways to detect these signals of TRA, from
the subtle to the prominent.
