Speaker
Prof.
Erik Aurell
(KTH Computational Biology)
Description
The entropy change in the environment of a classical
stochastic system is an important
quantity which underlies the recent extension of
thermodynamics to the mesoscopic domain.
It can be combined with the energy change in the system
to give a fluctuating work which enters in
the fluctuation relations, e.g. Jarzynski's equality, that hold
also far from equilibrium.
Generalization of this theory to the quantum domain are
not obvious, see Campisi et al
Rev Mod Phys vol 83 (2011) for a review, and Hekking &
Pekola Phys Rev Lett vol 111,
Horowitz & Parrondo New J. Phys vol 15 and Chetrite &
Mallick J Stat Phys vol 148
for a selection of more recent contributions.
Suppose that the quantum entropy change in the
environment is defined as the change of von
Neumann entropy in a bath, a proposal, in this context, due
to Esposito, Lindenberg and van den Broeck (2010).
Suppose further that the bath is comprised by a large
number of harmonic oscillators, linearly coupled to the
system, which is initially in thermal equilibrium. Suppose
finally that the change occurs between two
measurements on the system during a process when the
system interacts with the bath and is also driven externally.
Then the bath variables can be integrated out and the
entropy change computed by the method of Feynman
and Vernon. For an Ohmic bath (Caldeira-Leggett model at
high enough temperature) the entropy change has the
correct classical limit of minus (inverse temperature) *
(work done by the bath on the system). I will describe this
calculation and discuss the first corrections of the high-
temperature limit.
