Here proposed is a revised version of the scaling theory of equilibrium critical phenomena. This revised theory is based on hypotheses which differ only slightly from those set forth in original formulations. The conclusions reached are essentially equivalent to those of Stell's weak scaling theory. One obtains relations which require prior knowledge of three exponents for the derivation of the rest. An additional exponent, denoted w, enters certain relations containing exponents which pertain to the correlation function. This exponent must be greater than or equal to one in order to satisfy certain generally accepted inequalities. An argument for why w should be greater than or equal to one is formulable within the framework of the original hypotheses of scaling theory. While the revised theory has the drawback of containing an extra unknown, it is nevertheless capable of reconciling scaling theory with other theories of critical exponents.
Applying time-dependent driving is a basic way of quantum control. Driven systems show various dynamics as its time scale is changed due to the different amount of nonadiabatic transitions. The fast-forward scaling theory enables us to observe slow (or fast) time-scale dynamics during moderate time by applying additional driving. Here we discuss its application to nonadiabatic transitions. We derive mathematical expression of additional driving and also find a formula for calculating it. Moreover, we point out relation between the fast-forward scaling theory for nonadiabatic transitions and shortcuts to adiabaticity by counterdiabatic driving.