Prof. Erik Aurell (KTH Computational Biology)
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.