Pub Date : 2024-08-12DOI: 10.1103/physreve.110.024305
Samantha Linn, Sean D. Lawley, Bhargav R. Karamched, Zachary P. Kilpatrick, Krešimir Josić
Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased and hence make better choices. We obtain asymptotic expressions in the large population limit quantifying how agents' initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in nontrivial ways to determine the reliability of decisions in a group.
{"title":"Fast decisions reflect biases; slow decisions do not","authors":"Samantha Linn, Sean D. Lawley, Bhargav R. Karamched, Zachary P. Kilpatrick, Krešimir Josić","doi":"10.1103/physreve.110.024305","DOIUrl":"https://doi.org/10.1103/physreve.110.024305","url":null,"abstract":"Decisions are often made by heterogeneous groups of individuals, each with distinct initial biases and access to information of different quality. We show that in groups of independent agents who accumulate evidence the first to decide are those with the strongest initial biases. Their decisions align with their initial bias, regardless of the underlying truth. In contrast, agents who decide last make decisions as if they were initially unbiased and hence make better choices. We obtain asymptotic expressions in the large population limit quantifying how agents' initial inclinations shape early decisions. Our analysis shows how bias, information quality, and decision order interact in nontrivial ways to determine the reliability of decisions in a group.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"24 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physreve.110.024603
Daniel Escaff
Recently, it has been shown that purely anti-aligning interaction between active particles may induce a finite wavelength instability. The formed patterns display intricate spatiotemporal dynamics, suggesting the presence of chaos. Here, we propose a quasi-one-dimensional simplification of the particle interaction model. This simplified model allows us to deduce amplitude equations that describe the collective motion of the active entities. We show that these equations exhibit chaotic orbits. Furthermore, via direct numerical simulations of the particle's system, we discuss the pertinence of these amplitude equations approach for describing the particle's self-coordinated motions.
{"title":"Self-organization of anti-aligning active particles: Waving pattern formation and chaos","authors":"Daniel Escaff","doi":"10.1103/physreve.110.024603","DOIUrl":"https://doi.org/10.1103/physreve.110.024603","url":null,"abstract":"Recently, it has been shown that purely anti-aligning interaction between active particles may induce a finite wavelength instability. The formed patterns display intricate spatiotemporal dynamics, suggesting the presence of chaos. Here, we propose a quasi-one-dimensional simplification of the particle interaction model. This simplified model allows us to deduce amplitude equations that describe the collective motion of the active entities. We show that these equations exhibit chaotic orbits. Furthermore, via direct numerical simulations of the particle's system, we discuss the pertinence of these amplitude equations approach for describing the particle's self-coordinated motions.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"30 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1103/physreve.110.024121
Elena Rufeil Fiori, Christian Maes
We define the heat capacity for steady periodically driven systems and as an example we compute it for dissipative two-level systems where the energy gap is time-modulated. There, as a function of ambient temperature, the Schottky peak remains the dominant feature. Yet, in contrast with equilibrium, the quasistatic thermal response of a nonequilibrium system also reveals kinetic information present in the transition rates; e.g., the heat capacity depends on the time-symmetric reactivities and changes by the presence of a kinetic barrier. It still vanishes though at absolute zero, in accord with an extended Nernst heat postulate, but at a different rate from the equilibrium case. More generally, we discuss the dependence on driving frequency and amplitude.
{"title":"Heat capacity of periodically driven two-level systems","authors":"Elena Rufeil Fiori, Christian Maes","doi":"10.1103/physreve.110.024121","DOIUrl":"https://doi.org/10.1103/physreve.110.024121","url":null,"abstract":"We define the heat capacity for steady periodically driven systems and as an example we compute it for dissipative two-level systems where the energy gap is time-modulated. There, as a function of ambient temperature, the Schottky peak remains the dominant feature. Yet, in contrast with equilibrium, the quasistatic thermal response of a nonequilibrium system also reveals kinetic information present in the transition rates; e.g., the heat capacity depends on the time-symmetric reactivities and changes by the presence of a kinetic barrier. It still vanishes though at absolute zero, in accord with an extended Nernst heat postulate, but at a different rate from the equilibrium case. More generally, we discuss the dependence on driving frequency and amplitude.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"65 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-09DOI: 10.1103/physreve.110.024602
Kyle T. Sullivan, Ryan C. Hayward, Gregory M. Grason
In geometrically frustrated assemblies local intersubunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here we use theory and coarse-grained simulation to study a recently developed class of “curvamer” particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both intraparticle shape deformation as well as compliance of interparticle cohesive gaps, an effect we can attribute to a finite range of attraction between particles. We show that the ratio of intraparticle (bending elasticity) to interparticle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly bound, curvature-focusing stacks at small size to gap opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intracurvamer stiffness. The finite range of interparticle attraction determines the range of cohesion in stacks that are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multiparticle scales.
{"title":"Self-limiting stacks of curvature-frustrated colloidal plates: Roles of intraparticle versus interparticle deformations","authors":"Kyle T. Sullivan, Ryan C. Hayward, Gregory M. Grason","doi":"10.1103/physreve.110.024602","DOIUrl":"https://doi.org/10.1103/physreve.110.024602","url":null,"abstract":"In geometrically frustrated assemblies local intersubunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here we use theory and coarse-grained simulation to study a recently developed class of “curvamer” particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both <i>intraparticle</i> shape deformation as well as compliance of <i>interparticle</i> cohesive gaps, an effect we can attribute to a <i>finite range of attraction</i> between particles. We show that the ratio of intraparticle (bending elasticity) to interparticle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly bound, curvature-focusing stacks at small size to gap opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intracurvamer stiffness. The finite range of interparticle attraction determines the range of cohesion in stacks that are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multiparticle scales.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"22 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-08DOI: 10.1103/physreve.110.024116
Raz Halifa Levi, Yacov Kantor
We consider a -dimensional correlated percolation problem of sites not visited by a random walk on a hypercubic lattice for , 4, and 5. The length of the random walk is . Close to the critical value , many geometrical properties of the problem can be described as powers (critical exponents) of , such as , which controls the strength of the spanning cluster, and , which characterizes the behavior of the mean finite cluster size . We show that at the ratio between the mean mass of the largest cluster and the mass of the second largest cluster is independent of and can be used to find . We calculate from the dependence of and , and from the finite size scaling of . The resulting exponent remains close to 1 in all dimensions. The exponent decreases from in to in
我们考虑一个 d 维的相关渗滤问题，即在 d=3、4 和 5 的超立方晶格 Ld 上，随机行走未访问的点的渗滤问题。随机行走的长度为 N=uLd。在临界值 u=uc 附近，问题的许多几何特性都可以用 uc-u 的幂次（临界指数）来描述，如控制跨簇强度的 β 和描述平均有限簇大小 S 行为的 γ。我们证明，在 uc 时，最大簇 M1 的平均质量与第二大簇 M2 的质量之比与 L 无关，可以用来求出 uc。我们根据 M1 和 M2 与 L 的关系计算出 β，并根据 S 的有限大小缩放计算出 γ。指数γ从 d=3 时的≈3.9 下降到 d=4 时的≈1.9 和 d=5 时的≈1.3，最终在 d=6 时达到预期的 γ=1，接近 γ=4/（d-2）。
{"title":"Critical exponents of correlated percolation of sites not visited by a random walk","authors":"Raz Halifa Levi, Yacov Kantor","doi":"10.1103/physreve.110.024116","DOIUrl":"https://doi.org/10.1103/physreve.110.024116","url":null,"abstract":"We consider a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi></math>-dimensional correlated percolation problem of sites <i>not</i> visited by a random walk on a hypercubic lattice <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>L</mi><mi>d</mi></msup></math> for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>d</mi><mo>=</mo><mn>3</mn></mrow></math>, 4, and 5. The length of the random walk is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"script\">N</mi><mo>=</mo><mi>u</mi><msup><mi>L</mi><mi>d</mi></msup></mrow></math>. Close to the critical value <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>u</mi><mo>=</mo><msub><mi>u</mi><mi>c</mi></msub></mrow></math>, many geometrical properties of the problem can be described as powers (critical exponents) of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>u</mi><mi>c</mi></msub><mo>−</mo><mi>u</mi></mrow></math>, such as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>β</mi></math>, which controls the strength of the spanning cluster, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math>, which characterizes the behavior of the mean finite cluster size <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>S</mi></math>. We show that at <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>u</mi><mi>c</mi></msub></math> the ratio between the mean mass of the largest cluster <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>1</mn></msub></math> and the mass of the second largest cluster <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>2</mn></msub></math> is independent of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi></math> and can be used to find <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>u</mi><mi>c</mi></msub></math>. We calculate <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>β</mi></math> from the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi></math> dependence of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>1</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>2</mn></msub></math>, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math> from the finite size scaling of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>S</mi></math>. The resulting exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>β</mi></math> remains close to 1 in all dimensions. The exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math> decreases from <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>≈</mo><mn>3.9</mn></mrow></math> in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>d</mi><mo>=</mo><mn>3</mn></mrow></math> to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>≈</mo><mn>1.9</mn></mrow></math> in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>d</mi><mo>=</mo><mn>4</mn","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"78 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-08DOI: 10.1103/physreve.110.l022601
Ana M. Montero, Andrés Santos
This study examines the transverse and longitudinal properties of hard disks confined in narrow channels. Employing an exact mapping of the system onto a one-dimensional polydisperse, nonadditive mixture of hard rods with equal chemical potentials, we compute various thermodynamic properties, including the transverse and longitudinal equations of state, along with their behaviors at both low and high densities. Structural properties are analyzed using the two-body correlation function and the radial distribution function, tailored for the highly anisotropic geometry of this system. The results are corroborated by computer simulations.
{"title":"Exploring anisotropic pressure and spatial correlations in strongly confined hard-disk fluids: Exact results","authors":"Ana M. Montero, Andrés Santos","doi":"10.1103/physreve.110.l022601","DOIUrl":"https://doi.org/10.1103/physreve.110.l022601","url":null,"abstract":"This study examines the transverse and longitudinal properties of hard disks confined in narrow channels. Employing an exact mapping of the system onto a one-dimensional polydisperse, nonadditive mixture of hard rods with equal chemical potentials, we compute various thermodynamic properties, including the transverse and longitudinal equations of state, along with their behaviors at both low and high densities. Structural properties are analyzed using the two-body correlation function and the radial distribution function, tailored for the highly anisotropic geometry of this system. The results are corroborated by computer simulations.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"38 10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-07DOI: 10.1103/physreve.110.024113
Andrew A. Allocca, Conner LeMaire, Thomas Iadecola, Justin H. Wilson
The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic -adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions can be made to coincide by varying a parameter in the model, producing a picture consistent with behavior observed in previous small-size numerical studies of the quantum model.
{"title":"Statistical mechanics of stochastic quantum control: d-adic Rényi circuits","authors":"Andrew A. Allocca, Conner LeMaire, Thomas Iadecola, Justin H. Wilson","doi":"10.1103/physreve.110.024113","DOIUrl":"https://doi.org/10.1103/physreve.110.024113","url":null,"abstract":"The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi></math>-adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions can be made to coincide by varying a parameter in the model, producing a picture consistent with behavior observed in previous small-size numerical studies of the quantum model.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"309 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-07DOI: 10.1103/physreve.110.024114
Johannes Schmidt, Andreas Schadschneider
The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings, we demonstrate scale invariance at different times and heights using large-scale Monte Carlo simulations of the totally asymmetric simple exclusion process, which belongs to the KPZ universality class. Here we focus on current (or height) fluctuations in the steady-state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial-state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by superdiffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.
{"title":"Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class","authors":"Johannes Schmidt, Andreas Schadschneider","doi":"10.1103/physreve.110.024114","DOIUrl":"https://doi.org/10.1103/physreve.110.024114","url":null,"abstract":"The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings, we demonstrate scale invariance at different times and heights using large-scale Monte Carlo simulations of the totally asymmetric simple exclusion process, which belongs to the KPZ universality class. Here we focus on current (or height) fluctuations in the steady-state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial-state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by superdiffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"66 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-07DOI: 10.1103/physreve.110.025303
Leheng Chen, Chuang Zhang, Jin Zhao
Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.
{"title":"Modeling heat conduction with dual-dissipative variables: A mechanism-data fusion method","authors":"Leheng Chen, Chuang Zhang, Jin Zhao","doi":"10.1103/physreve.110.025303","DOIUrl":"https://doi.org/10.1103/physreve.110.025303","url":null,"abstract":"Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"20 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-07DOI: 10.1103/physreve.110.024115
Peter Werner, Alexander K. Hartmann, Satya N. Majumdar
A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature and subject to an external force , which couples to the free length of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature and force , the full distribution of free lengths in the thermodynamic limit and show that it is qualitatively very different for , and . Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained already allows us to derive an analytical expression for the work distribution in the zipped phase for a long chain. We compute the large-deviation tails of the work distribution explicitly. This distribution can be interpreted as work distribution for an oscillatorylike model. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as with numerical simulations performed by applying sophisticated large-deviation algorithms.
我们引入了一个简单的拉链模型，以简化的方式表示折叠的 DNA 双螺旋或 RNA 中的发夹结构。双链发夹连接到温度为 T 的热浴中，并受到外力 f 的作用，该外力与未拉链序列的自由长度 L 相耦合。最左边的拉链位置可以看作是一个随机漫步者在一个特殊外场中的位置。在一个非常大的链的热力学极限中，增加力会导致在临界力 fc(T) 处出现拉链-解拉链的一阶相变。作为温度 T 和力 f 的函数，我们分析计算了热力学极限下自由长度的全分布 P(L)，并表明在 f<fc、f=fc 和 f>fc 时，自由长度的全分布有很大不同。接下来，我们将考虑力按照线性协议递增的准静态功过程。得到 P(L) 后，我们就可以推导出长链在拉链阶段 f<fc 的功分布 P(W) 的分析表达式。我们明确计算了工作量分布的大偏差尾部。该分布可解释为类似振荡模型的功分布。我们对功分布的分析结果与应用复杂的大偏差算法进行的数值模拟结果进行了比较。
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