Imperial College London
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Professor Grigorios A. Pavliotis

Faculty of Natural Sciences, Department of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Lucarini:2020:10.1098/rspa.2020.0688,
author = {Lucarini, V and Pavliotis, GA and Zagli, N},
doi = {10.1098/rspa.2020.0688},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
pages = {1--27},
title = {Response theory and phase transitions for the thermodynamic limit of interacting identical systems: Phase Transitions in Interacting Systems},
url = {http://dx.doi.org/10.1098/rspa.2020.0688},
volume = {476},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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.
AU  - Lucarini,V
AU  - Pavliotis,GA
AU  - Zagli,N
DO  - 10.1098/rspa.2020.0688
EP  - 27
PY  - 2020///
SN  - 1364-5021
SP  - 1
TI  - Response theory and phase transitions for the thermodynamic limit of interacting identical systems: Phase Transitions in Interacting Systems
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2020.0688
UR  - https://royalsocietypublishing.org/doi/full/10.1098/rspa.2020.0688
VL  - 476
ER  -
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