You are referring to Landauer’s principle with the "minimum amount of entropy associated with a single irreversible bit flip". While it is proven (or "trivial"

You are referring to Landauer’s principle with the "minimum amount of entropy associated with a single irreversible bit flip". While it is proven (or "trivial" if you believe some scientists on the subject), its applicability to all possible computation systems is not clear. Recent theory and experiment have re-emerged to study this field both in the classical and quantum regimes. See http://arxiv.org/PS_cache/physics/pdf/0210/0210005v2.pdf http://arxiv.org/PS_cache/physics/pdf/0210/0210005v2.pdf for a nice review and "Breakdown of the Landauer bound for information erasure in the quantum regime" (http://pre.aps.org/abstract/PRE/v64/i5/e056117 http://pre.aps.org/abstract/PRE/v64/i5/e056117) for a specific case.