Live-blogging from STATPHYS26 /1

Active Brownian motion, Clemens Bechinger. Chemotaxix, phototaxis, rheotaxis, gravitaxis: means by which bacteria sense gradients. Active motion by local demixing is their technique to produce active matter: the usual particles with the two emispheres covered by different metals. There is a critical temperature below which these particles perform ordinary Brownian motion. By lighting them up, they perform self-diffusophoresis due to the effect that the particle has on its surrounding environment. They menage for example to form mixtures of passive and active particles. Even 10% of active particles are sufficient to create clusters – as if they were dogs surrounding herds of sheep. There is some theoretical modelling but it’s not clear what’s the relationship to the experiments.

Coarsening kinetics, Leticia Cugliandolo. Coarsening happens where you quench, you change some parameters in a statistical model. She considers classical open systems, with stochastic dissipative dynamics, one heat bath, out of equilibrium (in which sense?). A quench is an abrupt (or slow) change of a coupling parameter, in the environment or in the system. She considers quenches between two equilibrium phases, through a phase transition. She shows an experimental picture, showing a mixture of compounds separating into phases, and keeps referring what people in companies and industry are interested in. The theory is the stochastic dynamics of the 2d Ising model after an instantaneous quench from high to low temperature, from paramagnet to ferromagnet. To give dynamics one turns a single spin with Monte-Carlo rule $p = 1, e^-\beta \Delta E, 1/2$ if $\Delta E >, <,=0$. Another rule would be the Voter model, with no Hamiltonian [Clifford & Sudbury etc.]. At the initial time one picks each spin with either +-1 with probability 1/2, no particular structure. At zero temperature, the Monte-Carlo simulation gives huge domains in the phase-ordering kinetic. At the critical temperature, the domains are rougher and much richer in fluctuations (and similarly in the Voter model). Dynamic scaling is a framework to study spatial patterns. In the phase ordering kinetics, there is a typical length $\ell = \xi_d(t) \sim t^{1/z_d}$, where I don’t know what’s the exponent. In the dynamics (at T= 0), when yet one round of updating of all the spins has not occurred, there appears a percolating cluster from one end to another end (I wonder though if this is not always the case for such an initial state). She gives some facts about critical percolation: in 2D on a torus, one can also have cross-percolation along the two fundamental cycles, of diagonal percolation; there exist formulas for the variance of the interface curvature. Next, she has to make the point that critical percolation occurs in this 2D Ising dynamics. What one observes that such percolation structures appear very early in the evolution, and at some point some of these clusters establish themselves and remain until the end of the dynamics, where the clusters become all homogeneous zones (at T=0). She argues that it is really critical percolation via some computational measurements (but no theoretical argument). The time for reaching critical percolation is $t_p \sim L^{z_p}$. She did not discuss the more interesting dynamics at the critical temperature.

An interesting question would be to study the steady-state dynamics and thermodynamics of a Glauber Ising model coupled to two heat reservoirs, one above and one below the critical temperature. An engine ensues.

Brownian Carnot Engine, J. Parrondo. A brief historical excursus on Carnot cycles, with the interesting story that first Carnot defined efficiency and only then Kelvin introduced the entropy. He then introduced the experiment that I know very well (and that finds sign of my own theory, the double peak).

Boundary-driven open systems, F. Barra. [see Spohn and Lebowitz ACP 38 (1978)]. Considers an open quantum system coupled to two reservoirs, going to the Lindblad. He has a current operator! How is it defined? [see Prosen PRL 107, 2011]. He has some sort of paradox but I didn’t understand: apparently the current operator has zero expectation which you don’t want (maybe because this current is a total differential?), which then means this is not a true nonequilibrium steady state (but is that true? I wonder…). Then he has to consider a boundary driven system, where only the last “spins” (if it is a spin chain) are coupled to the reservoirs [Linden, Popescu, Skryzypczyk, PRL 105, 2010]. He further assumes local detailed balance and all.

Nonequilibrium Rydberg atoms, R. Gutierrez (with Garrahan). A hamiltonian with strong interactions, giving rise to a master equation with interactions, Rabi oscillations (unitary) and a Lindbladian for dephasing. He talks about a Nakajuma-Zwanzig projecton operator technique for the solution of the master equation, interesting!

Self-consistent approach to thermal transport, D. He. [Lepri, Livi, Politi, Phys. Rep. 2003] Theories for thermal conduction: – kinetic theory – linear response – nonequilibrium methods (system+bath). In the last case, one considers an harmonic chain and puts it in contact with two heat baths, either by master equation methods or by Non-Equilibrium Green function methods. He shortly discusses the advantages and disadvantages of the two. They use the Caldeira-Legget model and calculate expression such as the Landauer formula in terms of the transition coefficient. All these methods are interesting but the talk didn’t manage to communicate much.

Absorbing state phase transitions, Matteo Marcuzzi. There are up or down spins (active or inactive). An active site can either decay with rate $\Gamma$ or it can activate a neighbour with rate $\lambda$. Of course the totally decayed rate is absorbing. Hence, there is a phase transition between completely inactive and active phase, when branching rate is sufficienly strong $\lambda/\Gamma > (\lambda/\Gamma)_c$. It is a nonequilibrium phase transition [Broadbent and Hammersley, Lemoult Nat. Phys. 2016, etc.]. He considered the classical case, with branching and de-branching at the same rate, and he makes that sector of the theory an open quantum system by considering a Lindblad equation for the density matrix (so it is half-classical in the decay, and half-quantum in the branching). They employ the Margin-Siggia-Rose method to obtain an effective action of the theory. Therefore: Competing processes with absorbing states yield non-equilibrium phase transitions; Rydberg atoms may be used to realize them experimentally, at the quantum level; the phase transition is in a different universality class than directed percolation, but this I didn’t really understand [PRL 116, 245701 (2016)].

(it is interesting that there are these absorbing states; I am wondering whether deficient chemical networks might display boundary states that are absorbing in some sense – maybe not completely absorbing, but there might be two phases one “close to the boundary” and one “in the bulk” with a sharp transition, due to the fact that certain reactions are shut down)

Stochastic thermodynamics with electrons in a circuit, J. Pekola. Experiments, mostly on the Maxwell demon.

Quantum violation of the fluctuation-dissipation theorem, A. Shimizu. He says that for Kubo linear response function is the canonical time correlation, and that FDT the linear response function is the time correlation in equilibrium. Frankly I don’t understand the difference. Anyway, he wants to show that quantum measurement and its disturbance creates problems for FDR. Pre-measurement state: “thermal pure quantum state” (what is a thermal pure quantum state is a mystery to me, as a thermal state seems to be a mixed one) [but he has two PRLs] He performs a “quasiclassical measurement”. The idea though is interesting: you want the error on the measurement of the observable to be smaller than the fluctuation at equilibrium. But on the other hand, if the measurement becomes too precise the effect of the disturbance might be too high.I’m not sure their way of treating thermodynamics is the proper one. I’m wondering whether a sort of fluctuation-dissipation-sort of uncertainty relation (in the spirit of the uncertainty principle of Barato et al.) would hold. Apparently the author has a long story of publications on problems with the Green-Kubo formula. They also calculate corrections to the response function. He also finds the unintuitive relation that FDT is violated even in the classical regime. That’s because there are two different ways of taking the “classical” limit, on with the hbar, the other with the frequency. Spohn: ETH pure thermal state (Eigenstate Thermalization Hypothesis).*

Fibonacci family of dynamical universality classes, J. Schmidt. Two-time steady state correlation functions of interacting and noninteracting particle models have some scaling, and the function and the exponent are universal (for diffusions z=2 and f(x) is Gaussian, for the KPZ z = 3/2 and f(x) is tabulated). So the question one asks is what general classes are possible [PNAS 112, 12645]. One takes a general perturbation of the density and considers the time evolution of fluctuations via Nonlinear Fluctuating Hydrodynamics.

KPZ equation: a variational perspective, I Wio. Starts from a paper by Graham, “Macroscopic potentials, bifurcations and noise in dissipative systems”, where he discusses the importance of variational principles. Observation: KPZ is a true nonequilibrium processe in that the drift cannot be derived from a potential (well, that’s quite obvious to me…). Via the Hopf-Cole transformation he somehow manages to give a potential and a Lyapunov functional. There is a strange integration that I suspect is not independent of the path. The claim that he has a steady state distribution for the KPZ is highly suspect.

Normal and anomalous diffusion…R. Salgado-Garcia. Disordered models: random walks on disordered models, continuos dynamics with Brownian potentials, Gaussian force fields etc. One can model the potential as a Brownian motion itself.

Order and symmetry breaking…, P. Hurtado. Phase transitions at the fluctuating level. Usually: order + symmetry-breaking + non-analyticity in some thermodynamic potential. These ideas were recently extended to the realm of fluctuations: dynamic phase transitions in the large deviation functions, which again exhibit non-analyticity accompanied by order and symmetry-breaking phenomena. One good model is the KMP model. Again macroscopic fluctuation theory is invoked (though it is still not clear to me what the theory exactly says, even after trying to read the [Rev. Mov. Phys. 87, 593 (2015)]. Anyway:

$\partial_t + \nabla (- D(\rho)\nabla \rho + \sigma(\rho) E + \xi) = 0$

They give a large deviation function for this set of systems, and that’s well-known. Is this equation assumed or derived? Anyway, he tells that in some regimes the current FDR is Gaussian, but that this gaussianity breaks down somewhere (I didn’t understand what is the order parameter that brings the system beyond gaussianity).

Stochastic thermodynamics of many-body systems, A. Imparato. He studies efficiency at maximum power, where he only varies with respect to one parameter and keeps the other constant (I remember Seifert arguing that this is the reason why the claimed universality of Esposito and Van den Broeck is not very universal).

* Recently at a conference I complained about contradictions in terms in thermodynamics, where one uses terminology of isolated systems to talk about things that pertain to open systems, line in the formulation of the second law “the entropy of the Universe cannot decrease”, which I think is an empty statement. Looking up for ETH, the first thing I find is yet another example of such contradiction in terms:

Sergei Khlebnikov, Martin Kruczenski: Thermalization of isolated quantum systems, arXiv:1312.4612

So I am afraid this work also falls into a vast program whose philosophy and motivation is precisely orthogonal to my own. Apparently Tauber shares my point of view…