We develop and extend a method presented by Patinet, Vandembroucq, and Falk [ Phys. Rev. Lett. 117, 045501 (2016)] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.

Any decomposition of the total trajectory entropy production for Markovian systems has a joint probability distribution satisfying a generalized detailed fluctuation theorem, when all the contributing terms are odd with respect to time reversal. The expression of the result does not bring into play dual probability distributions, hence easing potential applications. We show that several fluctuation theorems for perturbed nonequilibrium steady states are unified and arise as particular cases of this general result. In particular, we show that the joint probability distribution of the system and reservoir trajectory entropies satisfy a detailed fluctuation theorem valid for all times.

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels is derived. One of these relations implies specific inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. While these inequalities have been derived before for age-controlled models with negligible mother-daughter correlations, we show that they also hold for a broad class of size-controlled models. We discuss the implications of this result for the interpretation of a recent experiment in which the growth of bacteria strains has been probed at the single-cell level.

We extend the definition of nonadiabatic entropy production given for Markovian systems by Esposito and Van den Broeck [Phys. Rev. Lett. 104, 090601 (2010)], to arbitrary non-Markov ergodic dynamics. We also introduce a notion of stability characterizing non-Markovianity. For stable non-Markovian systems, the nonadiabatic entropy production satisfies an integral fluctuation theorem, leading to the second law of thermodynamics for transitions between nonequilibrium steady states. This quantity can also be written as a sum of products of generalized fluxes and forces, thus being suitable for thermodynamics. On the other hand, the generalized fluctuation-dissipation relation also holds, clarifying that the conditions for it to be satisfied are ergodicity and stability instead of Markovianity. We show that in spite of being counterintuitive, the stability criterion introduced in this work may be violated in non-Markovian systems even if they are ergodic, leading to a violation of the fluctuation theorem and the generalized fluctuation-dissipation relation. Stability represents then a necessary condition for the above properties to hold and explains why the generalized fluctuation-dissipation relation has remained elusive in the study of non-Markov systems exhibiting nonequilibrium steady states. DOI: http://dx.doi.org/10.1103/PhysRevE.86.031117 ©2012 American Physical Society

We study, using exact numerical simulations, the statistics of the longest excursion $l_{\text{max}}\left(t\right)$ up to time $t$ for the fractional Brownian motion with Hurst exponent $0<H<1$. We show that in the large $t$ limit, $⟨l_{\text{max}}\left(t\right)⟩\propto Q_{\infty }t$, where $Q_{\infty }\equiv Q_{\infty }\left(H\right)$ depends continuously on $H$. These results are compared with exact analytical results for a renewal process with an associated persistence exponent $\theta =1-H$. This comparison shows that $Q_{\infty }\left(H\right)$ carries the clear signature of non-Markovian effects for $H\ne 1/2$. The preasymptotic behavior of $⟨l_{\text{max}}\left(t\right)⟩$ is also discussed. DOI: http://dx.doi.org/10.1103/PhysRevE.81.010102 © 2010 The American Physical Society