  Recent criticisms (Shenker 2000 [in Other Internet Resources], Norton 2005) focussed upon whether heat generation must necessarily be associated with logically irreversible operations. A particular objection raised by Shenker and a similar objection by Norton, concerned the use of probability distributions over macroscopically distinct states. Both Shenker and Norton argued that the thermodynamic entropy of a system is only properly defined by considering the region of state space accessible to the given microstate. For physical representations of logical states it is essential that the physical system cannot jump from one logical state to another. Consequently, regions of state space corresponding to different logical states are not accessible to one another, or as Shenker referred to it, they are not interaccessible. In Landauer's original paper, he simply identified the p ln p term of the probability distribution over the distinct logical states with thermodynamic entropy. More developed Gibbsian approaches still calculate the Gibbs entropy of a statistical distribution over regions of state space which are not interaccessible.  Norton argued in detail that this is an illegitimate calculation, and that the resulting entropy has nothing to do with thermodynamic entropy.