Comment on ``Both site and link overlap distributions are non trivial in 3-dimensional Ising spin glasses'', cond-mat/0608535v2

We comment on recent numerical experiments by G.Hed and E.Domany [cond-mat/0608535v2] on the quenched equilibrium state of the Edwards-Anderson spin glass model. The rigorous proof of overlap identities related to replica equivalence shows that the observed violations of those identities on finite size systems must vanish in the thermodynamic limit. See also the successive version cond-mat/0608535v

Spin-Glass Stochastic Stability: a Rigorous Proof

We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in beta-average for both the Sherrington-Kirkpatrick model in terms of the square of the overlap function and for the Edwards-Anderson model in terms of the bond overlap. We show that the volume rate at which the property is reached in the thermodynamic limit is V^{-1}. As a byproduct we show that the stochastic stability identities coincide with those obtained with a different method by Ghirlanda and Guerra when applyed to the thermal fluctuations only.Comment: 12 pages, revised versio

Thermodynamic Limit for Mean-Field Spin Models

If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system with Hamiltonian $H_N$ verifies the condition $$\omega_N(H_N) \ge \omega_N(H_{N_1}+H_{N_2})$$ for every decomposition $N_1+N_2=N$, then its free energy density increases with $N$. We prove such a condition for a wide class of spin models which includes the Curie-Weiss model, its p-spin generalizations (for both even and odd p), its random field version and also the finite pattern Hopfield model. For all these cases the existence of the thermodynamic limit by subadditivity and boundedness follows.Comment: 15 pages, few improvements. To appear in MPE

Matching with shift for one-dimensional Gibbs measures

We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimization Strategies in Complex Systems

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the``greedy'' (quick decrease along the gradient) and the``reluctant'' (slow decrease close to the level curves) as well as those of a``stochastic convex interpolation''of the two. Concepts like the average relaxation time and the wideness of the attraction basin are analyzed and their system size dependence illustrated.Comment: 8 pages, 3 figure

Thermodynamical Limit for Correlated Gaussian Random Energy Models

Let \{E_{\s}(N)\}_{\s\in\Sigma_N} be a family of $|\Sigma_N|=2^N$ centered unit Gaussian random variables defined by the covariance matrix $C_N$ of elements \displaystyle c_N(\s,\tau):=\av{E_{\s}(N)E_{\tau}(N)}, and H_N(\s) = - \sqrt{N} E_{\s}(N) the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition $N=N_1+N_2$, and all pairs (\s,\t)\in \Sigma_N\times \Sigma_N: c_N(\s,\tau)\leq \frac{N_1}{N} c_{N_1}(\pi_1(\s),\pi_1(\tau))+ \frac{N_2}{N} c_{N_2}(\pi_2(\s),\pi_2(\tau)) where \pi_k(\s), k=1,2 are the projections of \s\in\Sigma_N into $\Sigma_{N_k}$. The condition is explicitly verified for the Sherrington-Kirckpatrick, the even $p$-spin, the Derrida REM and the Derrida-Gardner GREM models.Comment: 15 pages, few remarks and two references added. To appear in Commun. Math. Phy

Symmetries in Fluctuations Far from Equilibrium

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.Comment: 8 pages, 4 figure

Sampling rare fluctuations of height in the Oslo ricepile model

We have studied large deviations of the height of the pile from its mean value in the Oslo ricepile model. We sampled these very rare events with probabilities of order $10^{-100}$ by Monte Carlo simulations using importance sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf 73}, 021303, 2006] that in steady state of the Oslo ricepile model, the probability of large negative height fluctuations $\Delta h=-\alpha L$ about the mean varies as $\exp(-\kappa {\alpha}^4 L^3)$ as $L \to \infty$ with $\alpha$ held fixed, and $\kappa > 0$.Comment: 7 pages, 8 figure

Trichoderma harzianum cerato-platanin enhances hydrolysis of lignocellulosic materials

Considering its worldwide abundance, cellulose can be a suitable candidate to replace the fossil oil-based materials, even if its potential is still untapped, due to some scientific and technical gaps. This work offers new possibilities demonstrating for the first time the ability of a cerato-platanin, a small fungal protein, to valorize lignocellulosic Agri-food Wastes. Indeed, cerato-platanins can loosen cellulose rendering it more accessible to hydrolytic attack. The cerato-platanin ThCP from a marine strain of Trichoderma harzianum, characterized as an efficient biosurfactant protein, has proven able to efficiently pre-treat apple pomace, obtaining a sugar conversion yield of 65%. Moreover, when used in combination with a laccase enzyme, a notable increase in the sugar conversion yield was measured. Similar results were also obtained when other wastes, coffee silverskin and potato peel, were pre-treated. With respect to the widespread laccase pre-treatments, this new pre-treatment approach minimizes process time, increasing energy efficiency