Irreversibility in dynamical phases and transitions

Seara, Daniel S.; Machta, Benjamin B.; Murrell, Michael P.

doi:10.1038/s41467-020-20281-2

Cited by 38 publications

(35 citation statements)

References 59 publications

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“…We continue by comparing the heat rate from Equation (105) with the IEPR as introduced in Section 3 and used in previous works [9,54,64]. Substituting into Equation (105) the expression of ∇(δF /δφ) taken from the dynamics (85) yields…”

Section: Calculation Of the Heat Production Ratementioning

confidence: 99%

“…Given that the correction to Ṡ is given by an integral over space of I S→I (r, r), and that the latter is a divergence, one might speculate that there is no correction due to the Stratonovich to Itô transformation (at least for periodic boundary conditions). However, taking r 1 = r 2 in Equation ( 65), as required to evaluate Equation (64), produces an undefined δ(0) divergence. We, therefore, consider the entropy production rate of the fully discretised dynamics (61) and perform the same transformation from Stratonovich to Itô integral:…”

Section: Computing the Ieprmentioning

confidence: 99%

“…We continue by comparing the heat rate from Equation ( 105 ) with the IEPR as introduced in Section 3 and used in previous works [ 9 , 54 , 64 ]. Substituting into Equation ( 105 ) the expression of

taken from the dynamics ( 85 ) yields

where the IEPR

of the

dynamics reads [ 9 , 54 , 64 ]

(Note that for AMB, this equates by partial integration to Equations ( 59 ) and/or ( 68 ) given above.)…”

Section: Thermodynamics Of Active Field Theoriesmentioning

confidence: 99%

“…We continue by comparing the heat rate from Equation ( 105 ) with the IEPR as introduced in Section 3 and used in previous works [ 9 , 54 , 64 ]. Substituting into Equation ( 105 ) the expression of

taken from the dynamics ( 85 ) yields

where the IEPR

of the

dynamics reads [ 9 , 54 , 64 ]

(Note that for AMB, this equates by partial integration to Equations ( 59 ) and/or ( 68 ) given above.) Clearly, the second line in Equation ( 106 ) depends on the spurious drift terms, but it also depends directly on the evaluation of the stochastic integral

and thereby on the discretisation scheme used to evaluate the heat rate (including spatial discretisation).…”

Section: Thermodynamics Of Active Field Theoriesmentioning

confidence: 99%

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Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Cates

Fodor

Markovich

et al. 2022

Entropy

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Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself.

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Section: Calculation Of the Heat Production Ratementioning

confidence: 99%

Section: Computing the Ieprmentioning

confidence: 99%

“…We continue by comparing the heat rate from Equation ( 105 ) with the IEPR as introduced in Section 3 and used in previous works [ 9 , 54 , 64 ]. Substituting into Equation ( 105 ) the expression of

taken from the dynamics ( 85 ) yields

where the IEPR

of the

dynamics reads [ 9 , 54 , 64 ]

(Note that for AMB, this equates by partial integration to Equations ( 59 ) and/or ( 68 ) given above.)…”

Section: Thermodynamics Of Active Field Theoriesmentioning

confidence: 99%

“…We continue by comparing the heat rate from Equation ( 105 ) with the IEPR as introduced in Section 3 and used in previous works [ 9 , 54 , 64 ]. Substituting into Equation ( 105 ) the expression of

taken from the dynamics ( 85 ) yields

where the IEPR

of the

dynamics reads [ 9 , 54 , 64 ]

and thereby on the discretisation scheme used to evaluate the heat rate (including spatial discretisation).…”

Section: Thermodynamics Of Active Field Theoriesmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Cates

Fodor

Markovich

et al. 2022

Entropy

View full text Add to dashboard Cite

show abstract

“…It is perfectly possible in principle [33] that reversible dynamics does emerge after coarse graining even though the microscopic processes powering the dynamics of φ are very irreversible. However, the generic case in active matter is of course to have irreversible dynamics at the mesoscopic scale described by φ(r, t), and hence have positive IEPR in (58).…”

Section: A Informatic Entropy Productionmentioning

confidence: 99%

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Cates,

Fodor,

Markovich

et al. 2021

Preprint

View full text Add to dashboard Cite

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarsegrained stochastic partial differential equations carry a short-scale cutoff -which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing for simplicity on models with a purely diffusive scalar field, such as 'Model B' which describes phase separation in binary fluid mixtures. We address the requirement that the steady state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for 'active field theories' in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR) we must make a careful treatment of so-called 'spurious drift' and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative, via off-diagonal couplings to additional fields that encode thermodynamically the underlying chemical processes responsible for activity. In this case the spurious drift terms need careful accounting, not just to evaluate correctly the EPR, but also to numerically implement the Langevin dynamics itself.

show abstract

Dynamic transitions and Turing patterns of the Brusselator model

Muntari

Şengül

2022

Math Methods in App Sciences

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The dynamic transitions of the Brusselator model has been recently analyzed in Choi et al. (2021) and Ma and Wang (2011). Our aim in this paper is to address the relation between the pattern formation and dynamic transition results left open in those papers. We consider the problem in the setting of a 2D rectangular box where an instability of the homogeneous steady state occurs due to the perturbations in the direction of several modes becoming critical simultaneously. Our main results are twofold: (1) a rigorous characterization of the types and structure of the dynamic transitions of the model from basic homogeneous states and (2) the relation between the dynamic transitions and the pattern formations.We observe that the Brusselator model exhibits different transition types and patterns depending on the nonlinear interactions of the pattern of the critical modes.

show abstract

Irreversibility in dynamical phases and transitions

Cited by 38 publications

References 59 publications

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Dynamic transitions and Turing patterns of the Brusselator model

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