Open Markov Processes: A Compositional Perspective on Non-Equilibrium Steady States in Biology

@article{Pollard2016OpenMP,
title={Open Markov Processes: A Compositional Perspective on Non-Equilibrium Steady States in Biology},
author={Blake S. Pollard},
journal={Entropy},
year={2016},
volume={18},
pages={140}
}
In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These open Markov processes' serve as the building blocks for more complicated processes. In this paper, we describe the potential application of this framework in the modeling of biological systems as open systems maintained away from equilibrium. We show that non-equilibrium steady states emerge in open systems of…
11 Citations

Figures from this paper

We define the concept of an open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External
This work proposes a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain and shows that it is possible to describe the distribution of particles over the state space through the corresponding moment generating function.
• Computer Science, Mathematics
Entropy
• 2018
This work provides an accessible introduction to the maximum entropy Markov chain inference problem and large deviations theory to the community of computational neuroscience, avoiding some technicalities while preserving the core ideas and intuitions.
This thesis develops the theory of hypergraph categories and introduces the tools of decorated cospans and corelations, a more powerful version that permits construction of all hyper graph categories and hypergraph functors.
• Computer Science
• 2021
This paper focuses on modeling UML’s structural component, as exemplified by the class diagram using CT models, and argues that the use of CT in information modeling could make the authors' models less ambiguous, more precise, and more formal.
If $\mathbf{C}$ is a category with pullbacks then there is a bicategory with the same objects as $\mathbf{C}$, spans as morphisms, and maps of spans as 2-morphisms, as shown by Benabou. Fong has
• Materials Science
Entropy
• 2017
An entropy-based evaluation method, in which the uniformity of the contact strain-energy distribution is evaluated in three levels based on entropy, is developed to predict the assembly accuracy, and a comprehensive index is proposed.
We build a symmetric monoidal and compact closed bicategory by combining spans and cospans inside a topos. This can be used as a framework in which to study open networks and diagrammatic languages.
• Computer Science
Proceedings of the Royal Society A
• 2021
It is argued that operads provide an effective knowledge representation to address scalability challenges for complex system design and recent progress in effective modelling is described.
• Biology
Entropy
• 2018
The thermodynamic formalism is used to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain.

References

SHOWING 1-10 OF 30 REFERENCES

• Mathematics, Computer Science
• 2016
It is proved that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to open circuits made of linear resistors, and described how to “black box” an open Markov process.
• Mathematics
The Journal of chemical physics
• 2014
The steady state entropy production rate is decompose in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction.
• Biology
International journal of molecular sciences
• 2010
The stochastic, chemical master equation is developed as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment and it is suggested that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting.
• H. Qian
• Physics, Chemistry
The journal of physical chemistry. B
• 2006
A nonequilibrium statistical thermodynamic theory based on stochastic kinetics is introduced, mainly through a series of examples: single-molecule enzyme kinetics, nonlinear chemical oscillation, molecular motor, biochemical switch, and specificity amplification.
A general microscopic and macroscopic theory is developed for systems which are governed by a (linear) master equation. The theory is based on a network representation of the master equation, and the
In bistable systems the transition kinetics between the two locally stable states can be altered without changing the behavior in the immediate vicinity of the two favored steady states. It follows
1. Introduction.- 2. Models.- 2.1 The Purpose and Nature of Models.- 2.2 Enzyme-Catalyzed Reactions and the Michaelis-Menten Kinetics.- 2.3 Transport Across Membranes: A Black-Box Approach.- 2.4
A number of the theorems expounded by Prigogine, Glansdorff and their collaborators are translated into electrical circuit terminology and their validity and significance discussed. The simultaneous
1. Introduction and Summary.- 2. Dynamics and Work.- 3. Information Entropy.- 3.a Entropy and relative entropy.- 3.b Gibbs states.- 3.c Entropy-increasing processes.- 4. Heat Baths.- 5. Reversible