Information physics in cartoons

Rolf Landauer has done more than anyone else to establish the physics of information processing as a serious subject of scientific inquiry. Here I will take a less serious approach, highlighting his contributions to this field with the help of cartoons and diagrams drawn by himself and others. Landauer has always believed that physics and mathematics are profoundly interdependent (Fig. 1): on the one hand, the laws of physics are expressed in mathematical language; on the other, information can only be processed when it is embodied in a physical system. Perhaps because of its interdisciplinary nature, the physics of information has suffered more than its share of superficial thinking, exemplified by von Neumann’s remark in a 1949 lecture, posthumously published and made famous, that any computing device, natural or artificial, must dissipate at least kT ln 2 of energy ‘per elementary act of information, that is, per elementary decision of a two-way alternative, and per elementary transmittal of 1 unit of information’ [1]. Landauer’s traditional response to such pronouncements has been a cartoon (Fig. 2) suggesting that the problem of fundamental limits is too complex to be solved in a dinnertime discussion. Even in the more formal setting of scholarly books and papers, von Neumann’s principle has often been asserted as self-evident, or adduced from a few examples of particular mechanisms obeying it, without any effort to show that it must hold generally. Typically these mechanisms were optical, for example Brillouin’s argument [2] that a Maxwell’s demon, using light to observe molecules in flight, would need to expend at least one photon of energy at least kT to see the molecule against the background of blackbody radiation, or Gabor’s [3] transverse mode analysis of a light beam used to detect a molecule at one end of a long cylinder. We now know that von Neumann’s principle is too restrictive; it has been supplanted by Landauer’s principle, according to which the data processing operations have an irreducible thermodynamic cost if and only if they are logically irreversible. i.e. throw away information about the computer’s previous logical state. According to our current understanding [4–10], information acquisition or transmission need not be thermodynamically costly, but information destruction (e.g. when a Maxwell demon erases the result of one measurement to make room for the next) always is, and it is this cost which prevents the demon from violating the second law. The tendency of mid-twentieth century analyses of the demon to neglect the cost of information destruction, and concentrate instead on a supposed cost of information acquisition, probably represents a prejudice carried over from everyday life, where until recently information has been viewed as a valuable—or at worse worthless— commodity, not a waste product one would pay to have removed. It may also have been a side effect of the