Macroscopic fluctuation theory

Bertini, Lorenzo; Sole, Alberto De; Gabrielli, Davide; Jona-Lasinio, G.; Landim, Cláudio

doi:10.1103/revmodphys.87.593

Cited by 541 publications

(963 citation statements)

References 127 publications

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“…[31]. Similar approaches have been applied, under different names, to turbulence [32][33][34], stochastic reactions [35,36], diffusive lattice gases [37], and non-equilibrium surface growth [21-23, 25, 38-41] including the KPZ equation itself. The WNT equations can be formulated as a classical Hamiltonian field theory.…”

Section: Introductionmentioning

confidence: 99%

Short-time height distribution in the one-dimensional Kardar-Parisi-Zhang equation: Starting from a parabola

2016

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We study the probability distribution P(H, t, L) of the surface height h(x = 0, t) = H in the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimension when starting from a parabolic interface, h(x, t = 0) = x 2 /L. The limits of L → ∞ and L → 0 have been recently solved exactly for any t > 0. Here we address the early-time behavior of P(H, t, L) for general L. We employ the weak-noise theory -a variant of WKB approximation -which yields the optimal history of the interface, conditioned on reaching the given height H at the origin at time t. We find that at small H P(H, t, L) is Gaussian, but its tails are non-Gaussian and highly asymmetric. In the leading order and in a proper moving frame, the tails behave as − ln P = f+|H| 5/2 /t 1/2 and f−|H| 3/2 /t 1/2 . The factor f+(L, t) monotonically increases as a function of L, interpolating between time-independent values at L = 0 and L = ∞ that were previously known. The factor f− is independent of L and t, signalling universality of this tail for a whole class of deterministic initial conditions.

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Section: Introductionmentioning

confidence: 99%

Short-time height distribution in the one-dimensional Kardar-Parisi-Zhang equation: Starting from a parabola

2016

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“…In both cases, currents flow through the system, but only the conditioned ensemble respects the PT symmetry (27). This property of the conditioned ensemble has its origin in the symmetries of the underlying dynamics, which still have implications for rare fluctuations in which large currents are sustained over long time periods.…”

Section: Discussionmentioning

confidence: 99%

“…where the second equality is obtained by a change of integration variable and the third uses (24) and (27). Hence, on average, no energy flows into the heat bath in the steady state of the conditioned ensemble, even though a finite current J is flowing.…”

Section: Observable Consequencesmentioning

confidence: 99%

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

Jack

Kaiser

Zimmer

2017

Entropy

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Abstract:We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and driven out of equilibrium by non-conservative forces. We focus on the probabilities of rare events (large deviations). First, we discuss a PT (parity-time) symmetry that appears in ensembles of trajectories where a current is constrained to have a large (non-typical) value. We analyse the heat flow in such ensembles, and compare it with non-equilibrium steady states. Second, we consider pathwise large deviations that are defined by considering many copies of a system. We show how the probability currents in such systems can be decomposed into orthogonal contributions that are related to convergence to equilibrium and to dissipation. We discuss the implications of these results for modelling non-equilibrium steady states.

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“…The mathematical structure is identical to that of fluctuating heat [23] and/or mass [24] transport and the widely studied macroscopic fluctuation theory of fluids [25], where the scalar field ψ represents temperature [23] or number density fluctuations [24], while ξ (t) is the divergence of a heat or particle current. The symmetric tridiagonal matrixQ can be diagonalized by a linear transformation P −1Q P with an orthogonal matrix P which solely depends on the ratio ε/J .…”

Section: A Linear Spin-wave Theorymentioning

confidence: 99%

Energy repartition in the nonequilibrium steady state

2017

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The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are applicable to other thermodynamic systems such as Newtonian liquids, elastic solids, and Josephson junctions.

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Macroscopic fluctuation theory

Cited by 541 publications

References 127 publications

Short-time height distribution in the one-dimensional Kardar-Parisi-Zhang equation: Starting from a parabola

Short-time height distribution in the one-dimensional Kardar-Parisi-Zhang equation: Starting from a parabola

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

Energy repartition in the nonequilibrium steady state

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