|This paper examines the time-varying levels of weak-form efficiency and the presence of structural breaks for two worldwide crude oil benchmarks over the period spanning from January 2, 1990, through September 18, 2012. We use two different econophysics approaches for comparison purposes. The Hurst exponent is provided by the scaled range R/S analysis to measure the degree of long-range dependency exhibited by the West Texas Intermediate (WTI) and European Brent crude oil indices. The Shannon entropy approach, which is based on a symbolic time series analysis (STSA), allows a ranking of market-level efficiency. The empirical results show that the European Brent index is less inefficient than the WTI index for both methods. Moreover, we find that the Hurst exponent displays better performance than the Shannon entropy method. The Hurst exponent is also more effective than the Shannon entropy in detecting financial crashes and crises as well as extreme events, such as wars and terrorist attacks. These findings have several implications for commodity portfolio hedgers and risk managers.