A remarkable thesis prevails in the physics of information, saying that the logical properties of operations that are carried out by computers determine their physical properties. More specifically, it says that logically irreversible operations are dissipative by klog2 per bit of lost information. (A function is logically irreversible if its input cannot be recovered from its output. An operation is dissipative if it turns useful forms of energy into useless ones, such as heat energy.) This is Landauer's dissipation thesis, hereafter (...) LDT. LDT underlies and motivates numerous researches in physics and computer science. Nevertheless, this paper shows that is it plainly wrong. This conclusion is based on a detailed study of LDT in terms of the various notions of entropy used in main stream statistical mechanics. It is supported by a counter example for LDT. Further support is found in an analysis of the phase space representation on which LDT relies. This analysis emphasises the constraints placed on the choice of probability distribution by the fact that it has to be the basis for calculating phase averages corresponding to thermodynamic properties of individual systems. An alternative representation is offered, in which logical irreversibility has nothing to do with dissipation. The strong connection between logic and physics, that LDT implies, is thereby broken off. (shrink)