'It's the cost between what the machine is built for and what you use it for,' says Kolchinsky. The researchers call this a 'mismatch cost,' or the cost of being wrong. Kolchinsky and Wolpert have demonstrated that two computers might carry out the same calculation, for example, but differ in entropy production because of their expectations for inputs. If the computer carries out some other calculation, then it will generate additional entropy. The only way to achieve Landauer's minimum loss of energy, he says, is to design a computer with a certain task in mind. 'There's a cost that appears beyond Landauer's bound,' says Kolchinsky. Wolpert and Kolchinsky wanted to know: What is that energy cost of erasing information for a given system? Landauer derived an equation for the minimum amount of energy that is produced during erasure, but the SFI duo found that most systems actually produce more. 'If you erase a bit of information, you have to generate a little bit of heat,' says Kolchinsky. In 1961, IBM physicist Rolf Landauer discovered that when information is erased, as during such a calculation, the entropy of the calculator decreases (by losing information), which means the entropy of the environment must increase. From the answer alone, the machine can't report which pair of numbers acted as input. At the same time, the machine loses information about the input since not only 2+2 but also 3+1 (and other pairs of numbers) can produce the same output.

If a person inputs '2+2' into a calculator and then hits 'enter,' the computer outputs the answer-4. 'Computing systems are designed specifically to lose information about their past as they evolve,' says Wolpert.

Their latest exploration of the topic, published in Physical Review E, looks at applying these ideas to a wide range of classical and quantum areas, including quantum thermodynamics. The thermodynamics of computation is a research focus of physicist and SFI resident faculty member David Wolpert, and for the last few years he's been collaborating with Artemy Kolchinsky, physicist and former SFI postdoctoral fellow, to better understand the connection between thermodynamics and information processing in computation.

Example of second law of thermodynamics