Since the discovery of long-time tails, it has been clear that Fourier’s law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Lévy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profiles for a broad set of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier’s law holds even deep into the nonlinear regime. This allows to solve the macroscopic transport problem for this model, a solution which compares flawlessly with data and, interestingly, implies the existence of a bound on the heat current in terms of pressure. These results question the renormalization-group and mode-coupling universality predictions for anomalous Fourier’s law in 1d, offering a new perspective on transport in low dimensions.

We consider an isolated, macroscopic quantum system. Let H be a microcanonical "energy shell," i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace H eq of H such that dim H eq / dim H is close to 1. We say that a system with state vector ψ ∈ H is in thermal equilibrium if ψ is "close" to H eq . We show that for "typical" Hamiltonians with given eigenvalues, all initial state vectors ψ 0 evolve in such a way that ψ t is in thermal equilibrium for most times t. This result is closely related to von Neumann's quantum ergodic theorem of 1929.

We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short timescale compared to that for the neuron dynamics and it produces short-time synaptic depression. This is inspired in recent neurobiological findings that show that synaptic strength may either increase or decrease on a short timescale depending on presynaptic activity. We thus describe a mechanism by which fast presynaptic noise enhances the neural network sensitivity to an external stimulus. The reason is that, in general, presynaptic noise induces nonequilibrium behavior and, consequently, the space of fixed points is qualitatively modified in such a way that the system can easily escape from the attractor. As a result, the model shows, in addition to pattern recognition, class identification and categorization, which may be relevant to the understanding of some of the brain complex tasks.

Garrido and Hurtado Reply: In this Reply, we answer the Comment by Li et al.[1] on our Letter ''Simple Onedimensional Model of Heat Conduction which Obeys Fourier's Law'' [2]. In that Letter, we studied the conductivity of a one-dimensional chain of N hard-point particles with alternating masses, proving that Fourier's law holds in this system.First, Li et al. study the conductivity N as a function of the system size N. They conclude that, as they do not observe saturation of the curve N even for N 8000 [instead, they fit N N 0:33 for large N], the large-N limit of N, 1 , must be divergent. In contrast, our conclusion was that finite size effects on N were too strong to conclude on 1 . In particular, we were able to fit both divergent and saturating laws to our data, thus demonstrating that this kind of study does not yield conclusive information on the value of 1 . Other authors have arrived at the same conclusions [3]. Moreover, we can argue [2] that N 1 ÿ AN ÿ0:3 , so N 8000 is still far and away the asymptotic region. Hence, the fact that N in Li et al. data has not yet saturated for N 8000 does not involve a divergent conductivity.In their Comment, Li et al. also report measurements on the total energy current self-correlation function, Ct. They observe that Ct t ÿ , with 0:67, thus concluding, via the Green-Kubo formula, that 1 is divergent. However, Ct also shows important finite size effects [4]. In particular, two different long time regions appear, the first one decaying algebraically as Ct t ÿ1ÿ , with 0:3, and the latest one decaying as Ct t ÿ , with 0:88. It can be shown [4] that the first region (which yields a finite conductivity) is the relevant one in the thermodynamic limit, being the very long time decay Ct t ÿ , a result of finite size effects. It can also be shown that, contrary to the Li et al. claim, a close relation between Ct and the local energy current self-correlation, ct, exists; and it implies a common long time behavior of Ct and ct for our alternating masses system [4]. This system is believed to be ergodic [3]. Thus, it is hard to believe that a change on the initial condition can yield a different decay exponent for Ct measured in equilibrium, as Li et al. claim.Let us now speak about the energy partition between light and heavy particles. Contrary to Li et al. claims, our results on this matter do not disagree with those of Kato and Jou [5]. They found that, at the nonequilibrium stationary state of the open system, the average energy stored in heavy particles exceeds the average energy stored in light ones. On the other hand, in our Letter we studied how an energy pulse propagates through an isolated system,

Dynamical phase transitions (DPTs) in the space of trajectories are one of the most intriguing phenomena of nonequilibrium physics, but their nature in realistic high-dimensional systems remains puzzling. Here we observe for the first time a DPT in the current vector statistics of an archetypal two-dimensional (2d) driven diffusive system, and characterize its properties using macroscopic fluctuation theory. The complex interplay among the external field, anisotropy and vector currents in 2d leads to a rich phase diagram, with different symmetry-broken fluctuation phases separated by lines of 1 st -and 2 nd -order DPTs. Remarkably, different types of 1d order in the form of jammed density waves emerge to hinder transport for low-current fluctuations, revealing a connection between rare events and self-organized structures which enhance their probability.Introduction-The theory of critical phenomena is a cornerstone of modern theoretical physics [1, 2]. Indeed, phase transitions of all sorts appear ubiquitously in most domains of physics, from cosmological scales to the quantum world of elementary particles. In a typical 2 nd -order phase transition order emerges continuously at some critical point, as captured by an order parameter, signaling the spontaneous breaking of a symmetry and an associated non-analyticity of the relevant thermodynamic potential. Conversely, 1 st -order transitions are characterized by an abrupt jump in the order parameter and a coexistente of different phases [1, 2]. In recent years these ideas have been extended to the realm of fluctuations, where dynamical phase transitions (i.e. in the space of trajectories) have been identified in different systems, both classical [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and quantum [18][19][20][21]. Important examples include glass formers [22][23][24][25][26][27][28][29], micromasers and superconducting transistors [30,31], or applications such as DPT-based quantum thermal switches [32][33][34].DPTs appear when conditioning a system to have a fixed value of some time-integrated observable, as e.g. the current or the activity. The different dynamical phases correspond to different types of trajectories adopted by the system to sustain atypical values of this observable. Interestingly, some dynamical phases may display emergent order and collective rearrangements in their trajectories, including symmetry-breaking phenomena [5,[9][10][11], while the large deviation functions (LDFs) [35] controlling the statistics of these fluctuations exhibit nonanalyticities and Lee-Yang singularities [36][37][38][39][40][41][42][43] at the DPT reminiscent of standard critical behavior. This is a finding of crucial importance in nonequilibrium physics, as these LDFs play a role akin to the equilibrium thermodynamic potentials for nonequilibrium systems, where no bottom-up approach exists yet connecting microscopic dynamics with macroscopic properties [3, 4,44]. Moreover, the emergence of coherent structures associated * phurtado@onsager.ugr.es to rare f...