The minimal work cost of information processing

• Published in: Nature communications 2015-07, Vol.6 (1), p.7669-7669, Article 7669
• Main Authors: Faist, Philippe, Dupuis, Frédéric, Oppenheim, Jonathan, Renner, Renato
• Format: Article
• Language: English
• Subjects: 639/638/440/951; 639/705/258; 639/766/483/640; Humanities and Social Sciences; multidisciplinary; Science; Science (multidisciplinary)
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/ncomms8669

Irreversible information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer’s principle, is increasingly relevant today, as the energy dissipation of computing devices impedes the development of their performance. Here we determine the minimal work required to carry out any logical process, for instance a computation. It is given by the entropy of the discarded information conditional to the output of the computation. Our formula takes precisely into account the statistically fluctuating work requirement of the logical process. It enables the explicit calculation of practical scenarios, such as computational circuits or quantum measurements. On the conceptual level, our result gives a precise and operational connection between thermodynamic and information entropy, and explains the emergence of the entropy state function in macroscopic thermodynamics. Irreversible computation cannot be performed without a work cost, and energy dissipation imposes limitations on devices' performances. Here the authors show that the minimal work requirement of logical operations is given by the amount of discarded information, measured by entropy.