Free energy fluxes and the Kubo–Martin–Schwinger relation

Doyon, Benjamin; Durnin, Joseph

doi:10.1088/1742-5468/abefe3

Cited by 8 publications

(20 citation statements)

References 53 publications

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“…In this paper we derive the general, multi-component diffusive hydrodynamic equations accounting for generic force fields. This generalises the Euler-scale results of [9,30] to the diffusive order. We express all terms using appropriate Onsager coefficients, written as time-integrated correlation functions of generalised currents as in the Green-Kubo formula.…”

Section: Introductionsupporting

confidence: 83%

“…The condition (1.33) makes all Onsager terms in (1.17) cancel, however there generally remains a nontrivial Euler-scale evolution, which preserves entropy. The fully stationary solutions are those where ∂ x j w,i = j i,f , which imposes the constraint that µ 0 (x) is a constant in (1.33) [9,30,60]. If it is not, the resulting Euler-scale evolution exits the space of states (1.33), and diffusion then further increases entropy.…”

Section: Entropy Increase and Stationaritymentioning

confidence: 99%

“…The latter quantity can be rewritten in terms of the usual Onsager coefficients by employing the Kubo-Martin-Schwinger (KMS) relation [30,62]. This allows us to rewrite the expectation value of the commutator in any homogeneous, stationary GGE as…”

Section: Diffusive Hydrodynamics: Inhomogeneous Fieldsmentioning

confidence: 99%

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Diffusive Hydrodynamics of Inhomogenous Hamiltonians

Durnin,

De Luca,

De Nardis

et al. 2021

Preprint

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We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. We show that this equation predicts entropy increase and thermal states as the only stationary states. The equation applies to any hydrodynamic system with any number of local, PT-symmetric conserved quantities, in arbitrary dimension. It is fully expressed in terms of elements of an extended Onsager matrix. In integrable systems, this matrix admits an expansion in the density of excitations. We evaluate exactly its 2-particle-hole contribution, which dominates at low density, in terms of the scattering phase and dispersion of the quasiparticles, giving a lower bound for the extended Onsager matrix and entropy production. We conclude with a molecular dynamics simulation, demonstrating thermalisation over diffusive time scales in the Toda interacting particle model with an inhomogeneous energy field.

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Section: Introductionsupporting

confidence: 83%

Section: Entropy Increase and Stationaritymentioning

confidence: 99%

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Diffusive Hydrodynamics of Inhomogenous Hamiltonians

Durnin,

De Luca,

De Nardis

et al. 2021

Preprint

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“…We would like to mention that the average energy current has also played an important role in the development of the generalized hydrodynamics [29,30]. Related works can be found in [31][32][33][34].…”

Section: Methods 1 Factorization Formulamentioning

confidence: 99%

$\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas

Jiang

2022

SciPost Phys.

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\mathrm{T}\bar{\mathrm{T}}TT‾ deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which was first studied in the context of integrability in AdS/CFT. In this paper, we construct such deformations for yet another type of models, which describe a collection of particles moving in 1d and interacting in an integrable manner. The prototype of such models is the Lieb-Liniger model. This shows that such deformations can be defined for a very wide range of systems. We study the finite volume spectrum and thermodynamics of the \mathrm{T}\overline{\mathrm{T}}TT¯-deformed Lieb-Liniger model. We find that for one sign of the deformation parameter (\lambda<0)(λ<0), the deformed spectrum becomes complex when the volume of the system is smaller than certain critical value, signifying the break down of UV physics. For the other sign (\lambda>0)(λ>0), there exists an upper bound for the temperature, similar to the Hagedorn behavior of the \mathrm{T}\overline{\mathrm{T}}TT¯ deformed QFTs. Both behaviors can be attributed to the fact that \mathrm{T}\overline{\mathrm{T}}TT¯ deformation changes the size the particles. We show that for \lambda>0λ>0, the deformation increases the spaces between particles which effectively increases the volume of the system. For \lambda<0λ<0, \mathrm{T}\overline{\mathrm{T}}TT¯ deformation fattens point particles to finite size hard rods. This is similar to the observation that the action of \mathrm{T}\overline{\mathrm{T}}TT¯-deformed free boson is the Nambu-Goto action, which describes bosonic strings — also an extended object with finite size.

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“…Within this formalism, we also obtain a new, model-independent derivation of the flow equations that describe how thermodynamic quantities change under T T -deformations. We obtain the flow equations not only for the free energy, as is traditionally done, but also for the free energy fluxes [5,34], which generate average currents and are related to entropy fluxes. This extends previous results, and in particular the result [16] concerning flows under Smirnov-Zamolochikov deformations, as it gives the flow equations under arbitrary T T deformations, including the new deformations discussed here associated to quasi-local charges, and it provides the flow for the free energy flux as well.…”

Section: Introductionmentioning

confidence: 99%

The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations

2022

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We introduce an extension of the generalised T\bar{T}TT‾-deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary functional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.

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Free energy fluxes and the Kubo–Martin–Schwinger relation

Abstract: Free energy fluxes and the Kubo-Martin-Schwinger relation as clustering, and we show that it is mathematically rigorous in quantum spin chains.

Cited by 8 publications

References 53 publications

Diffusive Hydrodynamics of Inhomogenous Hamiltonians

Diffusive Hydrodynamics of Inhomogenous Hamiltonians

$\mathrm{T}\overline{\mathrm{T}}$-deformed 1d Bose gas

The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations

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