I’m at NORDITA for one of their great programs on stochastic thermodynamics and related topics. I’ll update this post as things happen.

**Myself**. I gave two short presentations, one on marginal thermodynamics, and then I presented some ideas on what is tight coupling far from equilibrium, and how it can help understand the interplay between efficiency and critical behavior. I also drafted some notes that I do not mind sharing with anybody who might be interested in doing something with this piece of technology. Stay tuned!

**Lacoste**. [In collaboratio with Lahiri, Nghe, Rosinberg] How to tell causation with respect to correlation? Three-point correlations is a standard method. He wants to go beyond that, using concepts from information theory, to apply it to molecular processes. The object they are interested in is called *transfer entropy *[Schreiber 2000], and is related to so-called Granger causality [Granger, 1969]. The definition is not very revealing on its own. You have an input time-series X and an output one Y, and you look at a quantity that quantifies the improvement in the prediction about the future of Y deduced by the past of X, disregarding what you already know about the past of Y. It looks a little bit similar to the stochastic entropy. It’s not easy to evaluate these quantities because they depend on a large number of variables. Binning methods are unreliable, and more advanced numerical methods must be used. Apart from that, they also consider the information flow, which is the time-shifted mutual information between y_t and x_{t+dt} in the limit of small shift. They are furthermore going to consider bipartite systems which factor the y- and the x- directions. They have an application of all this machinery to the Kalman filter. Some authors evaluated the transfer entropy rate in some cases [Horowitz and Sandberg 2014, Sagawa 2014]. Finally he has some cool images describing growth rate of cells, and the data come in the form or of a large number of short time series, which si a frequent situation in biology. I’m lost in the biological application, I’ll have to check it out more carefully.

**Kawai**, *Eigenseletcion and Quantum Thermodynamics of Small Systems Strongly Interacting with Environments*. Considers the Gibbs state and realizes it’s very special, as it’s diagonal in the energy eigenbasis, fully decohered, and so he asks whether there’s anything special about the energy eigenbasis [my take on this would be the other way around: that the decohered “equilibrium” state is the one that defines energy…]. Mentions a Von Neumann-Everett theory of measurement. Starting from a unitary evolution, he rewrites the dynamics of the system’s sub-density matrix \rho_S in terms of a new operator \eta_S and mentions that the whole problem is to find the latter (so far so good, it’s just a rewriting…). In the case Markovian approximations apply, as well known the latter is linear in the former and decoherence happens very fast. He doesn’t like this approach because he wants to find another way to justify decoherence in the energy eigenbasis. So he takes a model of two qubits coupled among themselves and with two heat baths. Goes through very difficult techniques, including one of the latest contributions by Kubo, and somehow manages to reduce the description to a four-state system of mixed qubits. He then considers a Bell basis and a pointer basis, and studies the behaviour of the steady state as a function of the coupling constant, showing that the pointer basis is more “stable” than the Bell basis. He analyzes entanglement in the Born-Markov approximation and in the case of strong coupling, and finally he shows that at strong coupling the heat disappears, which can be interpreted as a manifestation of the quantum Zeno effect.

**Rondoni**. An add-on to a previous talk he gave last week (I was not present then). Casimir has plenty of sentences such as “If a magnetic field is present, the Eq. (8), (10), and (12) are no longer valid, but must be replaced by…”. The time-reversal operation means the transformation t -> -t, p -> -p, B -> -B, sigma -> -sigma. This is common wisdom about magnetic fields and time reversal. My comment: 1) given that we are considering very different settings, viz. deterministic dynamical systems, or underdamped SDEs vs. discrete Markov processes, on the assumption that NESM is more universal than the framework; 2) Considering that in my theory, I notice that when one has control on the full theory Onsager symmetry is always present as a consequence of the Fluctuation Theorem (something I could not explain in my talk), and that instead it is broken for marginal observables; 3) Then I propose a program where one makes the external magnetic field into an internal variable, with its conjugate thermodynamic current, then makes such current into a hidden observable, and then considers the marginal theory for the remaining degrees of freedom. Question: will we observe the old-style inversion of the magnetic field?