Abe Nitzan began his talk mentioning a recent PRL, Quantum Thermodynamics: A Nonequilibrium Green’s Function Approach, which unfortunately, is not valid because the expressions it gives do not give the correct result in the equilibrium limit. This is shown in

Quantum thermodynamics of the driven resonant level model

Anton Bruch, Mark Thomas, Silvia Viola Kusminskiy, Felix von Oppen, and Abraham Nitzan

What is striking to me about both papers is that they consider a

**non-interacting**model, i.e. the Hamiltonian is quadratic in fermion operators and exactly soluble.

This shows just how far we are from any sort of theory of a realistic system, i.e. one with interactions and which is not integrable.

Phil Geissler gave a nice introduction to different theorems for fluctuations in the dissipation (defined as the difference between the entropy change and heat/temperature). The most general theorem is that due to Gavin Crooks and implies the Jarzynski inequality, the fluctuation theorem, and the second law of thermodynamics.

A key question is what sorts of non-equilibrium processes (protocols) minimise the dissipation and whether the distribution is Gaussian (it often is).

He then described near optimal protocols to invert the magnetisation in a two-dimensional Ising model.

Suri Vaikuntanathan talked about coupled (classical) master equation models for biomolecular networks that have mathematical similarities to an electronic Su-Schrieffer-Heeger model which is an one-dimensional example of a topological insulator.

The work is described in a preprint with A. Murugan, "Topologically protected modes in non-equilibrium stochastic systems".

This is potentially important because it may provide "a framework for how biochemical systems can use non equilibrium driving to achieve robust function."

David Limmer gave a nice talk which considered thermodynamics as a large deviation theory and how that can even have meaning out of equilibrium and there is a notion of an entropy, a "free energy" and a "temperature". His slides are here.

A key notion is to focus on ensembles of trajectories rather than a probability distribution function. There are two alternative computational strategies: transition path sampling and diffusion Monte Carlo (the cloning algorithm).

He considered several concrete examples, such as thermal conductivity in carbon nanotubes, and electrochemical processes at electrode-water interfaces.

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