  In this work we show how the concept of majorization in continuous
distributions can be employed to characterize chaotic, diffusive and quantum
dynamics. The key point lies in that majorization allows to define an intuitive
arrow of time, within a continuous dynamics, along with an associated majorized
Second Law which implies the standard Second Law of thermodynamics but not
viceversa. Moreover, mixing dynamics, generalized Fokker-Planck equations and
quantum evolutions are explored as majorized ordered chains along the time
evolution, being the stationary states the infimum elements.
