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Motivated by the recent proposed models of the information engine [D. Mandaland C. Jarzynski, Proc. Natl. Acad. Sci. 109, 11641 (2012)] and the informationrefrigerator [D. Mandal, H. T. Quan, and C. Jarzynski, Phys. Rev. Lett. 111,030602 (2013)], we propose a minimal model of the information pump and theinformation eraser based on enzyme kinetics. This device can either pumpmolecules against the chemical potential gradient by consuming the informationencoded in the bit stream or (partially) erase the information encoded in thebit stream by consuming the Gibbs free energy. The dynamics of this model issolved exactly, and the "phase diagram" of the operation regimes is determined.The efficiency and the power of the information machine is analyzed. Thevalidity of the second law of thermodynamics within our model is clarified. Ourmodel offers a simple paradigm for the investigating of the thermodynamics ofinformation processing involving the chemical potential in small systems.

Thermodynamics of Information Processing Based on Enzyme Kinetics: an Exactly Solvable Model of Information Pump