Speaker
Prof.
Shin-ichi Sasa
(The University of Tokio)
Description
The main purpose of my talk is to present a new operational
formulation for the cumulant generating function of
time-averaged current.
According to Einstein's fluctuation theory in equilibrium
statistical mechanics, the cumulant generating function of
extensive variable is related to a thermodynamic function,
which leads to the fluctuation response-relation. On the
other hand, in non-equilibrium statistical mechanics, the
fluctuation-dissipation theorem (FDT) for a current holds
in the linear response regime, but the cumulant generating
function of time-averaged current itself has never been
considered in an operational manner like
Einstein's fluctuation theory. Now, our formulation
claims that the first derivative of the cumulant generating
function is equal to the expectation value of the current in
a modified system with an extra force added, where the
modified system is characterized by a variational principle.
The formula reminds us of Einstein's fluctuation theory and
simultaneously it leads to the FDT when the linear response
regime is focused on.
In my talk, after quickly reviewing Einstein's fluctuation
theory (in a little bit fresh form), I explain the main
results of our formulation. Then, I mention similarities
of our formulation with previously known theories such as
the Donsker-Varadhan theory, the additivity principle, and
the least dissipation principle. Finally, I discuss the
range of the applicability of our formulation and some
applications.
This work was done in collaboration with Takahiro Nemoto.
See arXiv:1109.
Primary author
Prof.
Shin-ichi Sasa
(The University of Tokio)
