General anesthetics are known to cause depression of the freezing point of transitions in biomembranes. This is a consequence of ideal mixing of the anesthetic drugs in the membrane fluid phase and exclusion from the solid phase. Such a generic law provides physical justification of the famous Meyer-Overton rule. We show here that general anesthetics, barbiturates, and local anesthetics all display the same effect on melting transitions. Their effect is reversed by hydrostatic pressure. Thus, the thermodynamic behavior of local anesthetics is very similar to that of general anesthetics. We present a detailed thermodynamic analysis of heat capacity profiles of membranes in the presence of anesthetics. Using this analysis, we are able to describe experimentally observed calorimetric profiles and predict the anesthetic features of arbitrary molecules. In addition, we discuss the thermodynamic origin of the cutoff effect of long-chain alcohols and the additivity of the effect of general and local anesthetics.