In this paper, we introduce a quantile version of past entropy for order statistics and study some of its properties. It is shown that this measure uniquely determine the quantile function. Two nonparametric classes of distributions are also defined based on the proposed measure. The closure of these classes under increasing convex (concave) transformations and weighted variables are discussed. Moreover, a new stochastic order based on this measure is defined and some features of it are investigated. We give desirable conditions for a function of a random variable to have more quantile past entropy for order statistics than original random variable.