Absence of dissipation in trajectory ensembles biased by currents

Jack, Robert L.; Evans, R. M. L.

doi:10.1088/1742-5468/2016/09/093305

Cited by 14 publications

(29 citation statements)

References 46 publications

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“…This symmetry of conditioned path ensembles mirrors the main result of [11] (which applies to a related set of "biased" path ensembles). (We derived this symmetry for systems described by (3) but the discussion of this section generalises immediately to any system as long as the path measure satisfies P (TX) = P (X) = P (PX) and the current J τ satisfies J τ (TX) = −J τ (X) = J τ (PX).…”

Section: Ensembles and Pt-symmetrysupporting

confidence: 63%

“…This section builds on recent work by Jack and Evans [11], concerning dissipation in certain trajectory ensembles. The motivation for that work was a hypothesis [15] that properties of non-equilibrium steady states can be inferred by analysing a particular class of rare fluctuations that occur at equilibrium.…”

Section: Absence Of Dissipation In Conditioned Ensembles Of Trajectoriesmentioning

confidence: 98%

“…It was argued in [11] that these events are free from dissipation, in contrast to typical non-equilibrium steady states. In Section 3, we review this argument and present some new examples that illustrate the operation of the general principle.…”

Section: Outlinementioning

confidence: 99%

“…The generalisation to the case where the friction depends on the co-ordinates is straightforward but requires some heavier notation. These stochastic differential equations are equivalent to Langevin equations in physics: see [11] (Equations (2) and (3)), and replace (dW/dt) by η. With this choice the invariant measure (steady state probability distribution) π for the phase space point (q, p) satisfies [13] dπ(q, p)…”

Section: Model: Conservative Forcesmentioning

confidence: 99%

“…Hence we say that the conditioned ensemble is free from dissipation. On the other hand, note that all co-ordinates q i are even under T. In this case, the derivation (28) may be used to show that the averages of all co-ordinates that are odd in P must vanish in the conditioned ensemble, see [11] for specific examples.…”

Section: Observable Consequencesmentioning

confidence: 99%

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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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Section: Ensembles and Pt-symmetrysupporting

confidence: 63%

Section: Absence Of Dissipation In Conditioned Ensembles Of Trajectoriesmentioning

confidence: 98%

Section: Outlinementioning

confidence: 99%

Section: Model: Conservative Forcesmentioning

confidence: 99%

Section: Observable Consequencesmentioning

confidence: 99%

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Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

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Kaiser

Zimmer

2017

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Non-Dissipative Effects in Nonequilibrium Systems

Maes

2018

SpringerBriefs in Complexity

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Studying the role of activity parameters and the nature of time-symmetric pathvariables constitutes an important part of nonequilibrium physics, so we argue. The relevant variables are residence times and the undirected traffic between different states. Parameters are the reactivities, escape rates and accessibilities and how those possibly depend on the imposed driving. All those count in the frenetic contribution to statistical forces, response and fluctuations, operational even in the stationary distribution when far enough from equilibrium. As these time-symmetric aspects can vary independently from the entropy production we call the resulting effects non-dissipative, ranking among features of nonequilibrium that have traditionally not been much included in statistical mechanics until recently. Those effects can be linked to localization such as in negative differential conductivity, in jamming or glassy behavior or in the slowing down of thermalization. Activities may decide the direction of physical currents away from equilibrium, and the nature of the stationary distribution, including its population inversion, is not as in equilibrium decided by energy-entropy content. The ubiquity of non-dissipative effects and of that frenetic contribution in theoretical considerations invites a more operational understanding and statistical forces outside equilibrium appear to provide such a frenometry. I. INTRODUCTORY COMMENTSUpon opening a book or a review on nonequilibrium physics, if not exposed to specific models, we are often guided immediately to consider notions and quantities that conceptually remain very close to their counterparts in equilibrium and that are concentrating on dissipative aspects. We mean ideas from local equilibrium, from balance equations and from meditating about the nature of entropy production. Even in the last decades, while a fluctuation theory for nonequilibrium systems has been moving to the foreground, in the middle stood the fluctuations of the path-dependent entropy fluxes and currents. A good example of a collection of recent work is stochastic thermodynamics, which however arXiv:1603.05147v2 [cond-mat.stat-mech]

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Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity

Palmer

Speck

2017

The Journal of Chemical Physics

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We discuss Onsager's thermodynamic formalism for transport coefficients and apply it to the calculation of the shear modulus and shear viscosity of a monodisperse system of repulsive particles. We focus on the concept of extensive "distance" and intensive "field" conjugated via a Fenchel-Legendre transform involving a thermodynamic(-like) potential, which allows to switch ensembles. Employing Brownian dynamics, we calculate both the shear modulus and the shear viscosity from strain fluctuations and show that they agree with direct calculations from strained and non-equilibrium simulations, respectively. We find a dependence of the fluctuations on the coupling strength to the strain reservoir, which can be traced back to the discrete-time integration. These results demonstrate the viability of exploiting fluctuations of extensive quantities for the numerical calculation of transport coefficients.

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Absence of dissipation in trajectory ensembles biased by currents

Cited by 14 publications

References 46 publications

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

Non-Dissipative Effects in Nonequilibrium Systems

Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity

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