I am confused about column efficiency. In GC, plate count can only be determined isothermally. In HPLC, k' (or k) and plate count are not valid for solvent gradient conditions. Why? How do you measure/report retention factor and efficiency (or peak quality) for gradient analysis?

If you look back in the archives you'll see several lengthy discussions on this topic. Just to summarize: gradient conditions in HPLC are analogous to thermal gradients in GC. One can generate any efficiency you like by manipulating the timing and the slope of the gradient, rendering comparisons meaningless unless one is comparing exactly the same gradient on exactly the same instrument (even then, the calculated plate count really has no legitimate meaning but can be used for comparison). The parameter generally used in its place for gradients is peak capacity. In essence, if the gradient is at constant slope then the peak capacity represents the maximum number of components one could fit into the separation if each component were barely baseline resolved. Even peak capacity is of limited value, however, if one is using complex gradients since once again peak capacity can be manipulated depending upon the details of the gradient.