Heat Generation in Computational Processes

How much energy must be used in a computation? Landauer [1] answered to this question in 1961 as follows: “Logical irreversibility implies physical irreversibility” (p.186 in Ref. [1]) and requires a finite amount of heat generation. A data-erasing operation is generally irreversible and induces the heat generation, which corresponds to a cost of energy, kT ln 2/bit (at least), while a reversible operation such as copying can be free of any cost of energy. It seems that Landauer’s theory has been accepted widely since then [2,3]. Recently, however, Goto et al. disputed it and claimed that it is possible to erase information without producing heat generation by using Quantum Flux Parametron devices [4]. The controversy has lead us to a recognition of several problems which relate to the thermodynamics of computations and are still left unclear: During the computational processes, q1. when does the heat generation occur? q2. when is the energy consumed? q3. when does the entropy increase (and when does it decrease)? q4. how should the thermodynamic entropy of computational devices be defined?