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Response theory and phase transitions for the thermodynamic limit of interacting identical systems.

ABSTRACT: We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers-Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker-Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai-Zwanzig model and of the Bonilla-Casado-Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

SUBMITTER: Lucarini V

PROVIDER: S-EPMC7776973 | biostudies-literature | 2020 Dec

REPOSITORIES: biostudies-literature

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Response theory and phase transitions for the thermodynamic limit of interacting identical systems.

Lucarini Valerio V Pavliotis Grigorios A GA Zagli Niccolò N

Proceedings. Mathematical, physical, and engineering sciences 20201223 2244

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers-Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker-Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the ...[more]

PMID: 33402877

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Project description:The formation and crystal structure of the binary Cu3As phase have been re-investigated. Some physical properties were then measured on both single crystal and polycrystalline bulk. Cu3As melts congruently at 835 °C. At room temperature (RT), this compound has been found to crystallize in the hexagonal Cu3P prototype (hP24, P63cm) with lattice parameters: a = 7.1393(1) Å and c = 7.3113(1) Å, rather than in the anti HoH3-type (hP24, P-3c1) as indicated in literature. A small compositional range of 74.0-75.5 at.% Cu (26.0-24.5 at.% As) was found for samples synthesized at 300 and 400 °C; a corresponding slight understoichiometry is found in one out of the four Cu atomic sites, leading to the final refined composition Cu2.882(1)As. The present results disprove a change in the crystal structure above RT actually reported in the phase diagram (from γ' to γ on heating). Instead, below RT, at T = 243 K (-30 °C), a first-order structural transition to a trigonal low-temperature superstructure, LT-Cu3-xAs (hP72, P-3c1) has been found. The LT polymorph is metrically related to the RT one, having the c lattice parameter three times larger: a = 7.110(2) Å and c = 21.879(4) Å. Both the high- and low-temperature polymorphs are characterized by the presence of a tridimensional (3D) uncommon and rigid Cu sublattice of the lonsdaleite type (Cu atoms tetrahedrally bonded), which remains almost unaffected by the structural change(s), and characteristic layers of triangular 'Cu3As'-units (each hosting one As atom at the center, interconnected each other by sharing the three vertices). The first-order transition is then followed by an additional structural change when lowering the temperature, which induces doubling of also the lattice parameter a. Differential scanning calorimetry nicely detects the first low-temperature structural change occurring at T = 243 K, with an associated enthalpy difference, ΔH(TR), of approximately 2 J/g (0.53 kJ/mol). Low-temperature electrical resistivity shows a typical metallic behavior; clear anomalies are detected in correspondence to the solid-state transformations. The Seebeck coefficient, measured as a function of temperature, highlights a conduction of n-type. The temperature dependence of the magnetic susceptibility displays an overall constant diamagnetic response.

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Response theory and phase transitions for the thermodynamic limit of interacting identical systems.

Publications

Response theory and phase transitions for the thermodynamic limit of interacting identical systems.

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