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Perturbative large deviation analysis of non-equilibrium dynamics
KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.ORCID iD: 0000-0002-1252-2899
KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
2014 (English)In: Journal of the Physical Society of Japan, ISSN 0031-9015, E-ISSN 1347-4073, Vol. 83, no 8Article in journal (Refereed) Published
Abstract [en]

Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these large deviation principles are in general not known in closed form. We consider the problem of constructing successive approximations to an (unknown) large deviation functional and show that the non-equilibrium probability distribution the takes a Gibbs-Boltzmann form with a set of auxiliary (non-physical) energy functions. The expectation values of these auxiliary energy functions and their conjugate quantities satisfy a closed system of equations which can imply a considerable reduction of dimensionality of the dynamics. We show that the accuracy of the approximations can be tested self-consistently without solving the full non- equilibrium equations. We test the general procedure on the simple model problem of a relaxing 1D Ising chain. 

Place, publisher, year, edition, pages
Physical society of Japan, 2014. Vol. 83, no 8
Keyword [en]
Macroscopic fluctuation theory, perturbative large deviation, dynamics Ising chain.
National Category
Condensed Matter Physics
Research subject
URN: urn:nbn:se:kth:diva-165789DOI: 10.7566/JPSJ.83.084001ISI: 000339806400012ScopusID: 2-s2.0-84924898390OAI: diva2:808824
EU, FP7, Seventh Framework Programme

QC 20150505

Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2016-09-04
In thesis
1. Equilibrium and Dynamics on Complex Networkds
Open this publication in new window or tab >>Equilibrium and Dynamics on Complex Networkds
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Complex networks are an important class of models used to describe the behaviour of a very broad category of systems which appear in different fields of science ranging from physics, biology and statistics to computer science and other disciplines. This set of models includes spin systems on a graph, neural networks, decision networks, spreading disease, financial trade, social networks and all systems which can be represented as interacting agents on some sort of graph architecture.

In this thesis, by using the theoretical framework of statistical mechanics, the equilibrium and the dynamical behaviour of such systems is studied.

For the equilibrium case, after presenting the region graph free energy approximation, the Survey Propagation method, previously used to investi- gate the low temperature phase of complex systems on tree-like topologies, is extended to the case of loopy graph architectures.

For time-dependent behaviour, both discrete-time and continuous-time dynamics are considered. It is shown how to extend the cavity method ap- proach from a tool used to study equilibrium properties of complex systems to the discrete-time dynamical scenario. A closure scheme of the dynamic message-passing equation based on a Markovian approximations is presented. This allows to estimate non-equilibrium marginals of spin models on a graph with reversible dynamics. As an alternative to this approach, an extension of region graph variational free energy approximations to the non-equilibrium case is also presented. Non-equilibrium functionals that, when minimized with constraints, lead to approximate equations for out-of-equilibrium marginals of general spin models are introduced and discussed.

For the continuous-time dynamics a novel approach that extends the cav- ity method also to this case is discussed. The main result of this part is a Cavity Master Equation which, together with an approximate version of the Master Equation, constitutes a closure scheme to estimate non-equilibrium marginals of continuous-time spin models. The investigation of dynamics of spin systems is concluded by applying a quasi-equilibrium approach to a sim- ple case. A way to test self-consistently the assumptions of the method as well as its limits is discussed.

In the final part of the thesis, analogies and differences between the graph- ical model approaches discussed in the manuscript and causal analysis in statistics are presented.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. 189 p.
TRITA-CSC-A, ISSN 1653-5723 ; 2016:17
Statistical mechanics, complex networks, spin systems, non equilibrium dynamics, generalized belief propagation, message passing, cavity method, variational approaches
National Category
Other Physics Topics Physical Sciences
Research subject
urn:nbn:se:kth:diva-191991 (URN)978-91-7729-058-2 (ISBN)
Public defence
2016-09-09, Kollegiesalen, Brinellvägen 8, plan 4, Stockholm, 10:00 (English)

QC 20160904

Available from: 2016-09-04 Created: 2016-09-03 Last updated: 2016-09-05Bibliographically approved

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