  The origin of fast radio bursts (FRBs), the brightest cosmic explosion in
radio bands, remains unknown. We introduce here a novel method for a
comprehensive analysis of active FRBs' behaviors in the time-energy domain.
Using ``Pincus Index'' and ``Maximum Lyapunov Exponent'', we were able to
quantify the randomness and chaoticity, respectively, of the bursting events
and put FRBs in the context of common transient physical phenomena, such as
pulsar, earthquakes, and solar flares. In the bivariate time-energy domain,
repeated FRB bursts' behaviors deviate significantly (more random, less
chaotic) from pulsars, earthquakes, and solar flares. The waiting times between
FRB bursts and the corresponding energy changes exhibit no correlation and
remain unpredictable, suggesting that the emission of FRBs does not exhibit the
time and energy clustering observed in seismic events. The pronounced
stochasticity may arise from a singular source with high entropy or the
combination of diverse emission mechanisms/sites. Consequently, our methodology
serves as a pragmatic tool for illustrating the congruities and distinctions
among diverse physical processes.
