# Live-blogging from STATPHYS26 /4

Active matter, S. Ramaswamy. From a title like that one might expect a general overview on what is active matter and its properties. However the talk stirs soon towards a presentation of a simple system of Langevin equation, and the claim is made that “active matter is just a Langevin system”, which I find to be highly contrived [by the way, I already had this doubt from the Parma workshop, with respect to a talk by G. Gonnella on active particles modelled with Langevin equations: what I don’t understand is how it is possible that an external field would allow for the peculiar individual behavior of active particles, but indeed it might be the case and I just have to figure this out on my own. Surely, the system Gonnella was considering was more elaborate and complex than the one presented here]. Anyway, I don’t see how this theoretical model then has anything to do with the rest of the results presented in the talk.

Network geometry, Ginestra Bianconi. Simplicial complexes are used in quantum gravity [where they emerge from an underlying theory]. She wants to apply nonequilibrium ideas to network geometry. She makes the simplicial complex (or its underlying skeletal network) grow by adding stuff. The boundary of small-world networks scales like the volume, and she says they use the master equation, don’t know in which respect. They define a generalized degree which is the number of generalized multi-hedra that are incident to a given one [it appears that this has nothing to do with the Laplacian which I’m in love with]. It’s all a story of defining things, e.g. introducing an arbitrary probability for attachment, and with this rule they obtain growing structures – so basically it seems to me that they are defining an algorithm to build growing high-dimensional structures that are scale-free [by construction?].

Models of antibiotic action on bacterial growth, M. R. Evans. Active matter: self-propelled constituents [by this very definition I doubt that they can be described just in terms of external fields and noise]. Sometimes I have the impression that “active matter” is a new word for “automata”. Generally, active matter lives in non-equilibrium states exhibiting collective behavior, and don’t obey the fluctuation-dissipation theorem [is this consistent with modelling with Langevin equations for which FDR holds?]. Evans has a sort of Fokker-Planck equation where the motility depends itself on the distribution , so it’s non-linear and it cannot descend from the Langevin equation [see notes on the first talk today as about whether this is or isn’t possible.] Another model that he uses is random walkers with memory. So my question remains open: is it possible to model active matter with Langevin equations? From this talk it would seem that no.

Thermodynamics of the motility-induced phase separation, Solon et al. More active matter talks later: run and tumble particles, etc. moved by “internal forces” (what that means is still obscure to me). For microscopic models, hard-core repulsion with a potential [Fily and Marchetti PRL 2012, Stenhammar PRL 2013, Takatori et al. PRL 2014, Solon et al éR 2’15, Redner et al. PRL 2013, Mallory et al. PRE] or other. The Cahn-Hilliard equation can be used to understand liquid-gas phase separation in equilibrium. It is a very nonlinear equation for the density’s time evolution.

Collective behavior in animal groups, I. Giardina. Flocks of birds: global order, scale-free correlations, collective turns (two individuals are able to influence each other, even if they are far apart). Swarms of midges: no global order, no polarization, collective behavior is not related with anti-predatory behavior but to mating, still correlations show quasi-critical behavior and collective response. Collective turns are interesting because they can be monitored to study information propagation in animal groups. They turn because there is a predator, but not necessarily, they can also respond to noise. I really like this talk because it analyzes processes with “dynamical” concepts and it does not fill the analysis with pseudo-scientific concepts from equilibrium statistical mechanics. The track trajectories quite precisely (including oscillations due to flapping). There is first a linear propagation of the turning wave, like a normal wave, with a final damp; interestingly, it is four-times larger than the birds’ velocity, in the birds reference frame. There are several different velocities according to the event, and there is no clear dependence with respect to size of the flock etc. So the questions are: Why linear propagation, why weak attenuation, what is the propagation speed, and what triggers turning? As model of flocking is the Vicsek model $\partial_t \varphi = \nabla^2 \varphi + \xi$ (or a discrete version of this), where $\varphi$ is the angle (and here there is already some approximation). Dispersion relation $\omega = i J k^2$. This is not what they actually find, because the Vicsek model is not very reasonable because it requires immediate response of birds. So they have to keep in to account a rotational inertia and conservation laws, and they obtain a second-order pd.f., and in the limit of zero noise the rotational invariance of the system resists, one obtains $\omega = c_s k$ and $x=c_st$ which is what you expected (just because it’s a second-order wave equation). this also predicts that the speed can be expressed in terms of measurable quantities, so there is a clear-cut prediction of the theory. The fit is quite nice [Nature Phys. 10, 2014]. With simulations, they see that according to the Vicsek model if one makes one bird turn, the others don’t follow, and instead with inertia if one turns all others do as well (that’s really intriguing: would every bird be able to decide for all? What if he is half-crazy? Doesn’t this make it very unstable?). So what triggers spontaneous turns of the flock? Simple statmech arguments on spontaneous fluctuations don’t give such frequent turns.  Two things are different with respect to the Heisenberg model: the network is irregular, and interactions are not symmetric because of directionality, so the zero mode of the Laplacian (which gives the relaxation time) does not scale with N like in the Heisenberg model. [Personal note: after all I am somewhat intrigued by this use of spin models to study dynamical information such as currents.].

Serious work, good talk. The room was packed on occasion of this invited talk. By far one of the best things I’ve heard so far.

Searching for the Tracy-Widom distribution in non-equilibrium processes, H. Spohn. Vintage slides, great clarity, as usual. TASEP with preparation of all the particles on one side, and one can ask for the time-integrated current across the origin and look at the typical profile. Usual currents

$\Phi(0,t) \sim - t/4 + (\Gamma t)^{1/3} \xi_{TW}$

where the distribution $\xi_{TW}$ is a universal distribution (and the dependency on time to the one-third already tells you that there is no central-limit theorem).It is the distribution of the largest eigenvalue of GUE random matrices, Tracy-Widom 1994. In what sense it is universal? (while 1/4, and $\Gamma$ are model dependent). Does TW show up for 1-dimensional fluids? You have to look for it in a subtle way. He considers a model of a harmonic chain running with Hamiltonian dynamics and an initial domain wall, in search of a “rarefaction wave”. There is an hyperbolic conservation law in t,x space and becuase of this the current is a curl (in x-t space). Sort of. But I must confess I’m lost already.

Rigorous bound on energy absorption…, T. Mori. A formulation of ETH: Every energy eigenstate is locally indistinguishable from thermal equilibrium. $\langle \phi_a |O|\phi_a|\rangle = \langle O \rangle_{thermal}$. Floquest ETH: the temperature in the steady state should be infinite (?!).

Second order response theory, M. Kruger. An example of nonlinear response is nonlinear optics, where you have a powerful laser and one has the generation of a “second harmonic wave”. The system evolves along a path with some probability with action that can be separated into the symmetric part and the antisymmetric part, and as usual one considers the usual fluctuation dissipation part linear in the perturbation plus a second order term, where both the activity and the symmetric part appears (three-body correlation function). the question he asks is: is this quantity experimentally relevant? [Basu, Kruger, Lazarescu etc.] So apparently they did an experiment with a single colloidal particle performing Brownian motion, anharmonic overdamped oscillator, etc. As usual, these experiments exactly fit the theoretical framework of Stochastic Thermodynamics so we don’t expect anything strange to happen. The did the Fourier analysis of the response. It is not clear to me which data exactly they fit, but it seems to be a quite clean result.

Temperature response of nonequilibrium systems, M. Baiesi. Susceptibility to a change of one temperature in a system out of equilibrium. [Note: they use the overdamped equations with two baths, that we know don’t make too much sense]. The rest I already kind of know.

Thermodynamics of phase coexistence in nonequilibrium systems, R. Dickman. There are two systems that are able to exchange particles but such that the current ends up to be zero, and if one of them is a reservoir than you can use it to measure the chemical potential of the other (?). Driven lattice gas with nearest-neighbour exclusion interactions with a critical density. Katz-Lebowitz-Spohn model. But all is very vague.

Nonequilibrium thermodynamic potentials, G. Verley. I’m not too fond of the word “potential” applied to nonequilibrium systems, but if it allows people to make contact with what they know then let it be… Nice talk, very pedagogical: he managed to give an intuitive picture on what is the effect of changing the temperature of a system does on both the antisymmetric and the symmetric properties of a system. Interesting Onsager relations that I should take a look at in view of my upcoming work.