Information , Noise , and Energy Dissipation : Laws , Limits , and Applications

This chapter addresses various subjects, including some open questions related to energy dissipation, information, and noise, that are relevant for nanoand molecular electronics. The object is to give a brief and coherent presentation of the results of a number of recent studies of ours. 1 Energy Dissipation and Miniaturization It has been observed, in the context of Moore’s law, that the power density dissipation of microprocessors keeps growing with increasing miniaturization [1–4], and quantum computing schemes are not principally different [5, 6] for general-purpose computing applications. However, as we point out in Sect. 2 and seemingly in contrast with the above statements, the fundamental lower limit of energy dissipation of a single-bit-flip event (or switching event) is independent of the size of the system. Therefore, the increasing power dissipation may stem from the following practical facts [1–4]: • A larger number of transistors on the chip, contributing to a higher number of switching events per second; • lower relaxation time constants with smaller elements, allowing higher clock frequency and the resulting increased number of switching events per second; L.B. Kish (✉) ⋅ S.P. Khatri Department of Electrical and Computer Engineering, Texas A&M University, TAMUS 3128, College Station, TX 77843-3128, USA e-mail: Laszlokish@tamu.edu; Laszlo.Kish@ece.tamu.edu C.-G. Granqvist ⋅ G.A. Niklasson The Ångström Laboratory, Department of Engineering Sciences, Uppsala University, P.O. Box 534, SE-75121 Uppsala, Sweden F. Peper CiNet, NICT, Osaka University, 1-4 Yamadaoka, Suita, Osaka 565-0871,  Molecular Architectonics, Advances in Atom and Single Molecule Machines, DOI 10.1007/978-3-319-57096-9_2 27 • increasing electrical field and current density, because the power supply voltage is not scaled back to the same extent as the device size; and • enhanced leakage current and related excess power dissipation, caused by an exponentially increasing tunneling effect associated with decreased insulator thickness and increased electrical field. It is clearly up to future technology to approach the fundamental limits of energy dissipation as much as possible. It is our goal in this chapter to address some of the basic, yet often controversial, aspects of the fundamental limits for nanoand molecular electronics. Specifically, we deal with the following issues: • The fundamental limit of energy dissipation for writing a bit of information. This energy is always positive and characterized by Brillouin’s negentropy formula and our refinement for longer bit operations [7–10]. • The fundamental limits of energy dissipation for erasing a bit of information [7–12]. This energy can be zero or negative; we also present a simple proof of the non-validity of Landauer’s principle of erasure dissipation [11, 12]. • Thermal noise in the low-temperature and/or high-frequency limit, i.e., in the quantum regime (referred to as “zero-point noise”). It is easy to show that both the quantum theory of the fluctuation–dissipation theorem and Nyquist’s seminal formula are incorrect and dependent on the experimental situation [13, 14], which implies that further studies are needed to clarify the properties of zero-point fluctuations in resistors in electronics-based information processors operating in the quantum limit. 2 Fundamental Lower Limits of Energy Dissipation for Writing an Information Bit [7–10] Szilard [15] (in 1929, in an incorrect way) and Brillouin [16] (in 1953, correctly) concluded that the minimum energy dissipation H1 due to changing a bit of information in a system at absolute temperature T is given as