Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes

Faggionato, Alessandra; Gabrielli, Davide; Ribezzi-Crivellari, Marco

doi:10.1007/s10955-009-9850-x

Cited by 86 publications

(138 citation statements)

References 17 publications

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“…In this paper we suggest such a technique: a class of models known as piecewise deterministic Markov processes [13]. These generalise Markov Chains to include exactly the kind of deterministically-varying transition rates required by models of homeostatic behaviour and have found a wide variety of uses in biology [14,15,16,17] and physics [18,19], although they have not previously been used to study food intake or energy balance. We use this model class to create a flexible and intuitive stochastic model of feeding behaviour governed by stomach fullness.…”

Section: Introductionmentioning

confidence: 99%

The homeostatic dynamics of feeding behaviour identify novel mechanisms of anorectic agents

McGrath

Spreckley

Rodriguez

et al. 2019

Preprint

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Better understanding of feeding behaviour will be vital in reducing obesity and metabolic syndrome, but we lack a standard model that captures the complexity of feeding behaviour. We construct an accurate stochastic model of rodent feeding at the bout level in order to perform quantitative behavioural analysis. Analysing the different effects on feeding behaviour of PYY 3-36 , lithium chloride, GLP-1 and leptin shows the precise behavioural changes caused by each anorectic agent. Our analysis demonstrates that the changes in feeding behaviour evoked by the anorectic agents investigated not mimic satiety. In the ad libitum fed state during the light period, meal initiation is governed by complete stomach emptying, whereas in all other conditions there is a graduated response. We show how robust homeostatic control of feeding thwarts attempts to reduce food intake, and how this might be overcome. In silico experiments suggest that introducing a minimum intermeal interval or modulating gastric emptying can be as effective as anorectic drug administration.

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Section: Introductionmentioning

confidence: 99%

The homeostatic dynamics of feeding behaviour identify novel mechanisms of anorectic agents

McGrath

Spreckley

Rodriguez

et al. 2019

Preprint

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“…For the Markov chain then undergoes many jumps over a small time interval ∆t during which ∆x ≈ 0, and thus the relative frequency of each discrete state n is approximately ρ n (x). This can be made precise in terms of a law of large numbers for stochastic hybrid systems proven in [24,25]. In the following we will take either Σ = R or Σ = R + = [0, ∞).…”

Section: One-dimensional Stochastic Hybrid Systemmentioning

confidence: 99%

“…An important problem is then characterizing how the underlying stochastic process approaches this deterministic limit in the case of weak noise, 0 < ǫ ≪ 1. A rigorous mathematical approach to addressing this particular issue has recently been developed for stochastic hybrid systems using large deviation theory [23][24][25]. Such a theory provides a variational or action principle that can be used to solve first passage time problems associated with the escape from a fixed point attractor of the underlying deterministic system in the weak noise limit.…”

Section: Introductionmentioning

confidence: 99%

Feynman-Kac formula for stochastic hybrid systems

Bressloff

2017

Phys. Rev. E

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We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

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“…In many papers on dynamical systems with random switching, the switching rates are allowed to depend on the location of the process X, and it is only required that the transition mechanism on S be irreducible (see for instance [FGRC09], [BLBMZ12a] and [CH13]). We hope to simplify our exposition by not studying more general classes of switching systems.…”

Section: Definitions and Notationmentioning

confidence: 99%