Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

Baek, Yongjoo; Kafri, Yariv; Lecomte, Vivien

doi:10.1088/1742-5468/ab43d5

Cited by 7 publications

(5 citation statements)

References 94 publications

(160 reference statements)

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“…( 15) give Ψ(Λ) = −S tot /( s T ). Note that in the limit of T 1 the initial and final boundary conditions on the different fields do not play an important role, except for fixing the total particles mass ρ 0 (however, for an exception see [69]).…”

Section: Macroscopic Fluctuation Theorymentioning

confidence: 99%

Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

Agranov,

Ro,

Kafri

et al. 2022

Preprint

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We study the current large deviations for a lattice model of interacting active particles displaying a motility-induced phase separation (MIPS). To do this, we first derive the exact fluctuating hydrodynamics of the model in the large system limit. On top of the usual Gaussian noise terms the theory also presents Poissonian noise terms, that we fully account for. We find a dynamical phase transition between flat density profiles and sharply phase-separated traveling waves, and we derive the associated phase diagram together with the large deviation function for all phases, including the one displaying MIPS. We show how the results can be obtained using methods similar to those of equilibrium phase separation, in spite of the nonequilibrium nature of the problem.

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Section: Macroscopic Fluctuation Theorymentioning

confidence: 99%

Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

Agranov,

Ro,

Kafri

et al. 2022

Preprint

Self Cite

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“…Also, the mapping we have used could be related to other ones that have been found for the current LDFs [19,20] or for the steady-state large deviations [119,120]. Last, studies of the gap in the deformed evolution operator (which is in principle possible within the Bethe Ansatz approach) could shed light on the finite-time scalings close to a DPT, in the spirit of previous works in diffusive [121] and superdiffusive [122] models, or in so-called large-N models [55,123]. and periodic boundary conditions L + 1 ≡ 1 describes, for µ ∈ R and p > 0, q > 0 the fluctuations of the current Q of an ASEP of jump parameters p and q, with µ being the Lagrange multiplier associated with Q.…”

Section: Discussionmentioning

confidence: 75%

Mapping current and activity fluctuations in exclusion processes: consequences and open questions

Vanicat¹,

Bertin²,

Lecomte³

et al. 2020

Preprint

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Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar-Parisi-Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.

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“…Also, the mapping we have used could be related to other ones that have been found for the current LDFs [19,20] or for the steady-state large deviations [121,122]. Last, studies of the gap in the deformed evolution operator (which is in principle possible within the Bethe Ansatz approach) could shed light on the finite-time scalings close to a DPT, in the spirit of previous works in diffusive [123] and super-diffusive [124] models, or in so-called large-N models [55,125]. For instance, the gap of W for µ = s = 0 has been obtained [73,126,127] for the TASEP and the ASEP in the absence of Legendre parameter conjugated to the current or the activity, and has been found to scale as 1/L 3/2 at large L. It would be interesting to extend their computation to the case of the deformed Markov matrices we have considered.…”

Section: Discussionmentioning

confidence: 76%

Mapping current and activity fluctuations in exclusion processes: consequences and open questions

et al. 2021

Self Cite

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Considering the large deviations of activity and current in the Asymmetric Simple Exclusion Process (ASEP), we show that there exists a non-trivial correspondence between the joint scaled cumulant generating functions of activity and current of two ASEPs with different parameters. This mapping is obtained by applying a similarity transform on the deformed Markov matrix of the source model in order to obtain the deformed Markov matrix of the target model. We first derive this correspondence for periodic boundary conditions, and show in the diffusive scaling limit (corresponding to the Weakly Asymmetric Simple Exclusion Processes, or WASEP) how the mapping is expressed in the language of Macroscopic Fluctuation Theory (MFT). As an interesting specific case, we map the large deviations of current in the ASEP to the large deviations of activity in the SSEP, thereby uncovering a regime of Kardar--Parisi--Zhang in the distribution of activity in the SSEP. At large activity, particle configurations exhibit hyperuniformity [Jack et al., PRL 114, 060601 (2015)]. Using results from quantum spin chain theory, we characterize the hyperuniform regime by evaluating the small wavenumber asymptotic behavior of the structure factor at half-filling. Conversely, we formulate from the MFT results a conjecture for a correlation function in spin chains at any fixed total magnetization (in the thermodynamic limit). In addition, we generalize the mapping to the case of two open ASEPs with boundary reservoirs, and we apply it in the WASEP limit in the MFT formalism. This mapping also allows us to find a symmetry-breaking dynamical phase transition (DPT) in the WASEP conditioned by activity, from the prior knowledge of a DPT in the WASEP conditioned by the current.

show abstract

Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

Cited by 7 publications

References 94 publications

Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

Macroscopic Fluctuation Theory and Current Fluctuations in Active Lattice Gases

Mapping current and activity fluctuations in exclusion processes: consequences and open questions

Mapping current and activity fluctuations in exclusion processes: consequences and open questions

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