Luca Gammaitoni - The Physics of Computing

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This book is about the physics of computing that is not the same as the physics of computers.

Indeed, there are many good books that discuss in detail the functioning of modern computers, with specific reference to the physical principles that rule their operations and this book is not one of them. Here, we are not going to go through any description of semiconductor materials or leakage currents in the last generation of field-effect transistors. You will not be bored with the description of the MOS capacitor or with the lithographic technique required to squeeze more transistors inside the same microprocessor. If you are interested in these arguments, please do not read this book.

How is the physics of computing different from the physics of computers? Well, it is like to say that we are going to talk about the physics of planetary motion; i.e. we are not interested in the dynamics of Jupiter or Mars, but we want to focus our attention to those principles that govern the motion of any of the planets, ignoring the differences among them. In this sense, we are interested in dealing with the fundamental underlying principles (if any) that characterize the computing machines existed, existing and, by definition of fundamental underlying principles, that will ever exist in future.

Such an exaggerated ambition would require a clear and strong definition of what we mean with the words computing and computer. Well, we will try to get away with the following definitions: computing is what a computer does and computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically (source: Wikipedia). And we will give for granted that the reader knows what an arithmetic or logical operation is, although we will come back to this point later in the book. Based on these definitions, we can say that computing is merely carrying on a sequence of arithmetic and/or logic operations.

Thus, in this book, we will discuss the fundamental physics principles that rule ANY physical device built to carry on arithmetic and/or logic operations.

The author owes a debt of gratitude to all friends, colleagues, collaborators and students of Noise in Physical Systems (NiPS) Laboratory at the University of Perugia, for developing the vision which underlies the writing of this book. In particular, he wishes to thank Markus Buttiker, Giovanni Carlotti, Francesco Cottone, Davide Chiuchi, Alessandro Di Michele, Cristina Diamantini, Miquel Lopez-Suarez, Igor Neri, Marco Madami, Fabio Marchesoni, Maurizio Mattarelli, Carlo Presilla, Carlo Trugenberger, Helios Vocca and Angelo Vulpiani. Special thanks to Igor Neri for a careful reading of the ms.

The term computing comes from the Latin computare, a word composed by the union of cum (with) and putare (to evaluate in quantitative sense). Together they mean to evaluate quantitatively things, strict synonymous of calculating, another Latin originated word that we will consider later on. So, based on this understanding, we could say that computing something has to do with dealing with the quantitative aspects of things.

How do we do that? Since when we were kids, we had to deal with numbers. A number represents a feature of specific properties of ensembles of things. For example: a bunch of cookies in a basket comes with some properties. They are sweet, they may be warm or cold, they may be light or heavy and they may few or many. These properties are evaluated here qualitatively but, if we want to be more precise, we could specify how much these properties are in place. Given our basket of cookies, we can say that they are warm at the touch (more precisely their temperature is 42 C), light if we raise them (more precisely their weight is 320 g), they are many (more precisely they are ten). How do we establish these quantities?

This can be done once we set a unit of measure and a method to compare the same property in different baskets. Comparing is clearly the first attempt to deal with quantities and counting is a very basic comparison. Let us look at how we determine how many cookies are in the basket by performing the counting. We start with the first cookie that comes to hand, and we set our counter to one, and then we increase the counter by one unit for every other cookie in the basket, while marking or displacing the cookies that have already been counted, in order to avoid considering the same cookie more than once. For the counter, we could use our memory or, if we have too many cookies or a lousy memory, we could use some device. The first device that comes handy is our fingers. Things like cookies can have their