Synopsis: The demon is in the details

In the theory of statistical information processing, what is the minimum amount of energy needed to make a measurement and then erase its memory?
Synopsis figure
Illustration: T. Sagawa and M. Ueda, Phys. Rev. Lett. (2009)

In 1867, Maxwell proposed a thought experiment: A demon could play the role of a gatekeeper at an initially impermeable membrane separating two regions of gas in thermodynamic equilibrium. The demon would open and close a molecule-sized orifice in the membrane to only let faster-than-average molecules pass to one side of the membrane, while only allowing slower-than-average ones to the other side. This microscopic asymmetry would appear at the macroscopic level as a more ordered gas in a lower-entropy state—questioning the validity of the second law of thermodynamics.

Maxwell’s construction has spurred critical examination and reexamination of the foundations of statistical thermodynamics, with increasing awareness that a proper analysis must account for how feedback control is actually executed by the hypothetical demon. Following the lead of earlier foundational work in information theory, Takahiro Sagawa and Masahito Ueda at the University of Tokyo, Japan, report in Physical Review Letters the minimum energy cost of thermodynamic information processing within what they label as “information thermodynamics.” They have succeeded in establishing a lower bound for the total cost of making a measurement and erasing the memory of it, even though there are no lower bounds on the work required for either of these individual processes. The fundamental bound for their sum total is universal and depends only on the mutual information content between the measured system and the memory, which is used to store the results of the measurements.

One tentative way to view the advance is that Maxwell’s demon has now been integrated into the system. The edifice is a generalized information-thermodynamic one, where the operation of the demon is reconciled with the laws of “usual” thermodynamics and where, alas, there is yet again no free lunch. – Yonko Millev


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