Thermodynamics of feedback controlled systems.

We compute the entropy reduction in feedback controlled systems due to the repeated operation of the controller. This was the lacking ingredient to establish the thermodynamics of these systems, and in particular of Maxwell's demons. We illustrate some of the consequences of our general results by deriving the maximum work that can be extracted from isothermal feedback controlled systems. As a case example, we finally study a simple system that performs an isothermal information-fueled particle pumping.

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

[2]  F. Cao,et al.  Time-delayed feedback control of a flashing ratchet. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[4]  Brian R. Long,et al.  Realization of a feedback controlled flashing ratchet. , 2008, Physical review letters.

[5]  Caves.  Quantitative limits on the ability of a Maxwell demon to extract work from heat. , 1990, Physical review letters.

[6]  Heiner Linke,et al.  Feedback control in flashing ratchets , 2008 .

[7]  Martin Bier,et al.  The stepping motor protein as a feedback control ratchet , 2007, Biosyst..

[8]  Zurek,et al.  Comment on "Quantitative limits on the ability of a Maxwell demon to extract work from heat" , 1990, Physical review letters.

[9]  Lloyd,et al.  Use of mutual information to decrease entropy: Implications for the second law of thermodynamics. , 1989, Physical review. A, General physics.

[10]  M. Feito,et al.  Threshold feedback control for a collective flashing ratchet: threshold dependence. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  H. Linke,et al.  Effect of time delay on feedback control of a flashing ratchet , 2007, 0707.0901.

[12]  Francisco J Cao,et al.  Feedback control in a collective flashing ratchet. , 2004, Physical review letters.

[13]  Seth Lloyd,et al.  Information-theoretic approach to the study of control systems , 2001, physics/0104007.

[14]  J. Parrondo,et al.  Closed-loop control strategy with improved current for a flashing ratchet , 2005, cond-mat/0505125.

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

[16]  H. Touchette,et al.  Information and flux in a feedback controlled Brownian ratchet , 2009 .

[17]  Caves.  Information and entropy. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  A. Rex,et al.  Maxwell's demon 2: entropy, classical and quantum information, computing , 2002 .

[19]  Touchette,et al.  Information-theoretic limits of control , 1999, Physical review letters.

[20]  M. Feito,et al.  Information and maximum power in a feedback controlled Brownian ratchet , 2007 .

[21]  W. H. Zurek,et al.  Thermodynamic cost of computation, algorithmic complexity and the information metric , 1989, Nature.

[22]  C. P. Sun,et al.  Maxwell's demon assisted thermodynamic cycle in superconducting quantum circuits. , 2005, Physical review letters.

[23]  Zurek,et al.  Algorithmic randomness and physical entropy. , 1989, Physical review. A, General physics.

[24]  J. Bechhoefer.  Feedback for physicists: A tutorial essay on control , 2005 .