  The relation between time series irreversibility and entropy production has
been recently investigated in thermodynamic systems operating away from
equilibrium. In this work we explore this concept in the context of financial
time series. We make use of visibility algorithms to quantify in
graph-theoretical terms time irreversibility of 35 financial indices evolving
over the period 1998-2012. We show that this metric is complementary to
standard measures based on volatility and exploit it to both classify periods
of financial stress and to rank companies accordingly. We then validate this
approach by finding that a projection in principal components space of
financial years based on time irreversibility features clusters together
periods of financial stress from stable periods. Relations between
irreversibility, efficiency and predictability are briefly discussed.
