# (Im-)Proving Landauer's Principle

Landauer's Principle connects information processing and thermodynamics as it enforces a certain amount of heat dissipation during the logically irreversible erasure of information. We formulate in precise mathematical and microscopic terms the minimal setup for Landauer's Principle. Based on this, we give a proof of an improved version of the Principle, which is formulated in terms of an equality rather than inequality.

We then use this equality version to explicitly sharpen the usual Landauer bound in cases where the assisting reservoir is of finite size. The key technical element for this part is a new and tight lower bound on the relative entropy between two states in terms of their entropy difference and the dimension of the underlying space. The derived finite-size effects may be relevant for small thermodynamic devices such as error-correcting mechanisms. (joint work with Michael Wolf, arXiv:1304.0036 and arXiv:very.soon)