The idea of developing a thermodynamic theory of systems under an external feedback dates back to the origin of statistical physics when Maxwell made his famous gedanken experiment concerning the effect of a Demon with some information about the system and the effect on the thermodynamics of the system itself. Recently this branch of thermodynamics has got a rapid boost thank to fluctuation theorems [1, 2]. An interesting complementary perspective comes from a branch of information theory named Large deviation theory (LDT). LDT is the mathematical framework which copes with the probability of large fluctuations departing from the average ensemble values of statistical quantities. In particular LDT demonstrates that for a large class of probability density functions (PDF), defined on the phase space, the probability of having a fluctuation respect to the average value drops exponentially. The exponent is related to the Legendre-Fenchel transform of the scaled cumulant generating function [3]. It has been demonstrated that the LDT provides a very elegant way to derive the thermodynamic principles of maximum entropy and minimal free energy for the microcanonical and canonical ensemble respectively in thermodynamic equilibrium [4]. Extension to non equilibrium conditions have been investigated [5]. We present here an extension of the formalism that allows to use LDT also for systems under an external feedback, in particular we show how it is possible to define a direct connection between the measurement performed by the feedback and its accuracy and the maximum entropy reduction that can be achieved with that feedback. Moreover it will be shown how the formalism can actually be generalized in order to tackle also problems related to non equilibrium thermodynamics such as molecular junctions under an external bias.
[1] T. Sagawa and M. Ueda, Phys. Rev. E, 85, 021104 (2012).
[2] T. Sagawa and M. Ueda, Phys. Rev. Lett., 109, 180602 (2012).
[3] R.S. Ellis, Entropy, Large Deviations, and Statistical Mechanics, Springer, New York, 1985.
[4] H. Touchette, Physics Reports, 478, 169 (2009).
[5] H. Touchette, (Chapter 11), Non equilibrium Statistical Physics of small systems, Edited by R. Klages, W. Just and C. Jarzinsky; WyleyVCH, 2013.
The idea of developing a thermodynamic theory of systems under an external feedback dates back to the origin of statistical physics when Maxwell made his famous gedanken experiment concerning the effect of a Demon with some information about the system and the effect on the thermodynamics of the system itself. Recently this branch of thermodynamics has got a rapid boost thank to fluctuation theorems [1, 2]. An interesting complementary perspective comes from a branch of information theory named Large deviation theory (LDT). LDT is the mathematical framework which copes with the probability of large fluctuations departing from the average ensemble values of statistical quantities. In particular LDT demonstrates that for a large class of probability density functions (PDF), defined on the phase space, the probability of having a fluctuation respect to the average value drops exponentially. The exponent is related to the Legendre-Fenchel transform of the scaled cumulant generating function [3]. It has been demonstrated that the LDT provides a very elegant way to derive the thermodynamic principles of maximum entropy and minimal free energy for the microcanonical and canonical ensemble respectively in thermodynamic equilibrium [4]. Extension to non equilibrium conditions have been investigated [5]. We present here an extension of the formalism that allows to use LDT also for systems under an external feedback, in particular we show how it is possible to define a direct connection between the measurement performed by the feedback and its accuracy and the maximum entropy reduction that can be achieved with that feedback. Moreover it will be shown how the formalism can actually be generalized in order to tackle also problems related to non equilibrium thermodynamics such as molecular junctions under an external bias.
[1] T. Sagawa and M. Ueda, Phys. Rev. E, 85, 021104 (2012).
[2] T. Sagawa and M. Ueda, Phys. Rev. Lett., 109, 180602 (2012).
[3] R.S. Ellis, Entropy, Large Deviations, and Statistical Mechanics, Springer, New York, 1985.
[4] H. Touchette, Physics Reports, 478, 169 (2009).
[5] H. Touchette, (Chapter 11), Non equilibrium Statistical Physics of small systems, Edited by R. Klages, W. Just and C. Jarzinsky; WyleyVCH, 2013.
