The out-of-equilibrium dynamics of the Sherrington–Kirkpatrick model

Cugliandolo, Leticia F.; Kurchan, Jorge

doi:10.1088/1751-8113/41/32/324018

Cited by 16 publications

(30 citation statements)

References 63 publications

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“…This equation is known to be integrable (in particular, it presents infinitely many symmetries, a bi-Hamiltonian structure, solitary wave solution and an infinite number of conservation laws [66,74,83,85]). These two equations are the lowest elements of the so-called Burgers hierarchy, which can be presented in the form…”

Section: Few Words On Burgers Hierarchymentioning

confidence: 99%

PDE/Statistical Mechanics Duality: Relation Between Guerra’s Interpolated p-Spin Ferromagnets and the Burgers Hierarchy

Fachechi

2021

J Stat Phys

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We examine the duality relating the equilibrium dynamics of the mean-field p-spin ferromagnets at finite size in the Guerra’s interpolation scheme and the Burgers hierarchy. In particular, we prove that—for fixed p—the expectation value of the order parameter on the first side w.r.t. the generalized partition function satisfies the $$p-1$$ p - 1 -th element in the aforementioned class of nonlinear equations. In the light of this duality, we interpret the phase transitions in the thermodynamic limit of the statistical mechanics model with the development of shock waves in the PDE side. We also obtain the solutions for the p-spin ferromagnets at fixed N, allowing us to easily generate specific solutions of the corresponding equation in the Burgers hierarchy. Finally, we obtain an effective description of the finite N equilibrium dynamics of the $$p=2$$ p = 2 model with some standard tools in PDE side.

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Section: Few Words On Burgers Hierarchymentioning

confidence: 99%

PDE/Statistical Mechanics Duality: Relation Between Guerra’s Interpolated p-Spin Ferromagnets and the Burgers Hierarchy

Fachechi

2021

J Stat Phys

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“…In order to explain the relation between the multibath measure and the dynamics described in the previous section we recall the definition of effective temperature. Given the twotime correlations C(τ) of the spins and the associated response R(τ) and integrated response χ(τ) =´τ 0 R(τ − τ )dτ then the effective temperature can be defined by the relation [8,12,17] 1…”

Section: The Sk Model With a Multithermalized Random Fieldmentioning

confidence: 99%

“…To understand the meaning of this, following [8] we consider triangles of correlations at three large times t 1 < t 2 < t 3 . Scaling (49) implies:…”

Section: Timescales Of a Systemmentioning

confidence: 99%

Stationarization and Multithermalization in spin glasses

et al. 2021

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We develop further the study of a system in contact with a multibath having different temperatures at widely separated timescales. We consider those systems that do not thermalize in finite times when in contact with an ordinary bath but may do so in contact with a multibath. Thermodynamic integration is possible, thus allowing one to recover the stationary distribution on the basis of measurements performed in a `multi-reversible' transformation. We show that following such a protocol the system is at each step described by a generalization of the Boltzmann-Gibbs distribution, that has been studied in the past. Guerra's bound interpolation scheme for spin-glasses is closely related to this: by translating it into a dynamical setting, we show how it may actually be implemented in practice. The phase diagram plane of temperature vs ``number of replicas", long studied in spin- glasses, in our approach becomes simply that of the two temperatures the system is in contact with. We suggest that this representation may be used to directly compare phenomenological and mean-field inspired models. Finally, we show how an approximate out of equilibrium probability distribution may be inferred experimentally on the basis of measurements along an almost reversible transformation.

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“…To emphasize the fundamental difference of such additive corrections to the FDT, compared to those that one would naturally want to capture by an effective temperature, some researchers have given the name “frenesy” to the additional term appearing in the linear response . It has been suggested that the effective temperature might still be a sensible definition when the system evolves slowly, irrespectively of whether it relaxes or is in a steady state . Furthermore, Cugliandolo et al .…”

Section: Non‐equilibrium Brownian Thermometrymentioning

confidence: 99%

Brownian Thermometry Beyond Equilibrium

Geiß

Kroy

2019

ChemSystemsChem

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Since Albert Einstein's seminal 1905‐paper on Brownian motion, the temperature of fluids and gases of known viscosity can be deduced from observations of the fluctuations of small suspended probe particles. We summarize recent generalizations of this standard technique of Brownian thermometry to situations involving spatially heterogeneous temperature fields and other non‐equilibrium conditions in the solvent medium. The notion of effective temperatures is reviewed and its scope critically assessed. Our emphasis is on practically relevant real‐world applications, for which effective temperatures have been explicitly computed and experimentally confirmed. We also elucidate the relation to the more general concept of (effective) temperature spectra and their measurement by Brownian thermospectrometry. Finally, we highlight the conceptual importance of non‐equilibrium thermometry for active and biological matter, such as microswimmer suspensions or biological cells, which often play the role of non‐thermal (“active”) heat baths for embedded Brownian degrees of freedom.

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The out-of-equilibrium dynamics of the Sherrington–Kirkpatrick model

Cited by 16 publications

References 63 publications

PDE/Statistical Mechanics Duality: Relation Between Guerra’s Interpolated p-Spin Ferromagnets and the Burgers Hierarchy

PDE/Statistical Mechanics Duality: Relation Between Guerra’s Interpolated p-Spin Ferromagnets and the Burgers Hierarchy

Stationarization and Multithermalization in spin glasses

Brownian Thermometry Beyond Equilibrium

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