cfaed Seminar Series

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. 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. 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. Extension to non equilibrium conditions have been investigated.
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.