Total cost of operating an information engine

We study a two-level system controlled in a discrete feedback loop, modeling both the system and the controller in terms of stochastic Markov processes. We find that the extracted work, which is known to be bounded from above by the mutual information acquired during measurement, has to be compensated by an additional energy supply during the measurement process itself, which is bounded by the same mutual information from below. Our results confirm that the total cost of operating an information engine is in full agreement with the conventional second law of thermodynamics. We also consider the efficiency of the information engine as a function of the cycle time and discuss the operating condition for maximal power generation. Moreover, we find that the entropy production of our information engine is maximal for maximal efficiency, in sharp contrast to conventional reversible heat engines.

[1]  Henrik Sandberg,et al.  Maximum work extraction and implementation costs for nonequilibrium Maxwell's demons. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  John D. Norton,et al.  Exorcist XIV: The wrath of maxwell’s demon. Part II. from szilard to Landauer and beyond , 1999 .

[3]  Udo Seifert,et al.  An autonomous and reversible Maxwell's demon , 2013, 1302.3089.

[4]  A. C. Barato,et al.  Information-theoretic vs. thermodynamic entropy production in autonomous sensory networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  C. Broeck,et al.  Thermodynamic efficiency at maximum power. , 2005 .

[6]  Masahito Ueda,et al.  Fluctuation theorem with information exchange: role of correlations in stochastic thermodynamics. , 2012, Physical review letters.

[7]  L. Szilard.  über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen , 1929 .

[8]  John D. Norton,et al.  Exorcist XIV: The Wrath of Maxwell’s Demon. Part I. From Maxwell to Szilard , 1998 .

[9]  F. Curzon,et al.  Efficiency of a Carnot engine at maximum power output , 1975 .

[10]  D. Andrieux,et al.  Fluctuation theorem and Onsager reciprocity relations. , 2004, The Journal of chemical physics.

[11]  J. Koski,et al.  Experimental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon. , 2014, Physical review letters.

[12]  Jordan M Horowitz,et al.  Imitating chemical motors with optimal information motors. , 2012, Physical review letters.

[13]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[14]  Masahito Ueda,et al.  Second law of thermodynamics with discrete quantum feedback control. , 2007, Physical review letters.

[15]  Massimiliano Esposito,et al.  Universality of efficiency at maximum power. , 2009, Physical review letters.

[16]  J. Schnakenberg.  Network theory of microscopic and macroscopic behavior of master equation systems , 1976 .

[17]  Udo Seifert,et al.  Rate of Mutual Information Between Coarse-Grained Non-Markovian Variables , 2013, 1306.1698.

[18]  Gernot Schaller,et al.  Thermodynamics of a physical model implementing a Maxwell demon. , 2012, Physical review letters.

[19]  Masahito Ueda,et al.  Nonequilibrium thermodynamics of feedback control. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  A. C. Barato,et al.  Unifying three perspectives on information processing in stochastic thermodynamics. , 2013, Physical review letters.

[21]  U. Seifert,et al.  Extracting work from a single heat bath through feedback , 2011, 1102.3826.

[22]  M. Planck.  Vorträge über die kinetische Theorie der Materie und der Elektrizität : gehalten in Göttingen auf Einladung der Kommission der Wolfskehlstiftung , 1914 .

[23]  Masahito Ueda,et al.  Generalized Jarzynski equality under nonequilibrium feedback control. , 2009, Physical review letters.

[24]  M. Sano,et al.  Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality , 2010 .

[25]  Udo Seifert.  Entropy production along a stochastic trajectory and an integral fluctuation theorem. , 2005, Physical review letters.