There are various situations where prior information is available on parameters in the form of order relations. One needs to take into account this information to obtain superior estimators. Shannon modeled uncertainty mathematically and called it entropy. In this paper, we study the problem of estimating entropy of two exponential populations associated with a common scale parameter, and unknown but ordered location parameters. In particular, the unrestricted best affine equivariant estimator is shown to be inadmissible under order restricted location parameters with respect to a class of location invariant loss functions. Under some specific location invariant loss functions, various improved estimators are obtained. Applications of this problem are developed for various sampling schemes: (i) i.i.d. sampling, (ii) record values, (iii) Type-II censoring and (iv) progressive Type-II censoring. Numerically, we have compared the risk performance of the proposed estimators for the squared error and linex loss functions.