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Separable equilibrium state probabilities via time reversal in Markovian process algebra

P.G. Harrison, T.T. Lee
2005 Theoretical Computer Science  
The reversed compound agent theorem (RCAT) is a compositional result that uses Markovian process algebra (MPA) to derive the reversed process of certain interactions between two continuous time Markov  ...  From this reversed process, together with the given, forward process, the joint state probabilities can be expressed as a product-form, although no general algorithm has previously been given.  ...  As stated in the introduction, the goal is to find separable solutions for the equilibrium probabilities in a stationary Markov process by using its reversed process.A reversed process is actually just  ... 
doi:10.1016/j.tcs.2005.08.007 fatcat:flbctbypmjbc3gtqxhkcuicmca

Page 1543 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
In Chapter 4, matrix algebra, for a finite system of equations in Laplace transforms, is used to obtain transient state probabilities for Markovian queues with finite waiting room.  ...  The number of customers in the system is treated directly, which gives explicit expressions for the transient state probabilities in M/M/1/N via Chebyshev polynomials.  ... 

Turning Back Time--What Impact on Performance?

P. G. Harrison
2009 Computer journal  
The joint probability distribution of the sojourn times of a tagged task at each node in a network is determined by noting that this is the same in both the forward and reversed processes.  ...  In this way, existing results for response time probability densities in tandem, tree-like, and overtake-free Markovian queueing networks are quickly and systematically obtained.  ...  We apply a completely different approach to the computation of the LSTs of response times in Markovian networks at equilibrium, via joint sojourn time distributions and using reversed processes.  ... 
doi:10.1093/comjnl/bxp021 fatcat:clyc2mxjtbfinjqllyq4nifxsa

Exploiting Quasi-reversible Structures in Markovian Process Algebra Models

P. Harrison
1995 Computer journal  
Markovian process algebras (MPA) extend classical process algebras with information about the duration of actions but retain their compositional structure: a system is modelled as an interaction of components  ...  This work uses the notion of quasi-reversibility in a Markov process setting to de ne the type of interaction between MPA components.  ...  Structures in Markovian Process Algebra Models 3 subprocess r", and similarly for departures.  ... 
doi:10.1093/comjnl/38.7.510 fatcat:3t3j77xvjngmpinlnxxgzdyrwy

Simultaneous computation of dynamical and equilibrium information using a weighted ensemble of trajectories [article]

Ernesto Suarez, Steven Lettieri, Matthew C. Zwier, Carsen A. Stringer, Sundar Raman Subramanian, Lillian T. Chong, Daniel M. Zuckerman
2014 arXiv   pre-print
., 1996] to generate equilibrium trajectory ensembles and extract non-equilibrium subsets for computing kinetic quantities. States do not need to be chosen in advance.  ...  Many non-equilibrium processes can be described by suitable subsets of the equilibrium ensemble. Here, we employ the "weighted ensemble" (WE) simulation protocol [Huber and Kim, Biophys.  ...  Supporting Information Available Reference coordinates for the order parameters in Ala4, visualization of the states used in Ala4 (A1, A2, B1 and B2) and a comparison of the regular Markov model vs the  ... 
arXiv:1210.3094v2 fatcat:k32g2nojwncspfxy2or4xxoxw4

Simultaneous Computation of Dynamical and Equilibrium Information Using a Weighted Ensemble of Trajectories

Ernesto Suárez, Steven Lettieri, Matthew C. Zwier, Carsen A. Stringer, Sundar Raman Subramanian, Lillian T. Chong, Daniel M. Zuckerman
2014 Journal of Chemical Theory and Computation  
We also describe a related history-dependent matrix procedure for estimating equilibrium and nonequilibrium observables when phase space has been divided into arbitrary non-Markovian regions, whether in  ...  J. 1996, 70, 97−110] to generate equilibrium trajectory ensembles and extract nonequilibrium subsets for computing kinetic quantities. States do not need to be chosen in advance.  ...  unit time arriving at state B in the α steady state, and p(α) is the total probability in the α steady state.  ... 
doi:10.1021/ct401065r pmid:25246856 pmcid:PMC4168800 fatcat:bp7ygcwcxfbw3pt4h7k7cis4ge

Process Algebraic Non-product-forms

P.G. Harrison
2006 Electronical Notes in Theoretical Computer Science  
A generalization of the Reversed Compound Agent Theorem of Markovian process algebra is derived that yields separable, but non-product-form solutions for collections of interacting processes such as arise  ...  The extended methodology leads to what we believe are new separable solutions and, more generally, the results represent a viable practical application of the theory of Markovian process algebras in stochastic  ...  The Reversed Compound Agent Theorem (RCAT) is a compositional result that uses Markovian process algebra (MPA) to derive the reversed process of certain cooperations between two continuous time Markov  ... 
doi:10.1016/j.entcs.2006.03.012 fatcat:uyf5ikzm5jau7kbcpi4gk5v764

Author index

2005 Theoretical Computer Science  
Lee, Separable equilibrium state probabilities via time reversal in Markovian process algebra (1) 161-182 Hayes, I.J., see K. Lermer (1) 3-27 Herman, G.T., see E. Gardun˜o (2-3) 281-299 Hurd, J., A.  ...  Hayes, A theory for execution-time derivation in realtime programs (1) 3-27 Leroux, P., see D. Gouyou-Beauchamps (2-3) 307-334 Lluch-Lafuente, A. and U.  ... 
doi:10.1016/s0304-3975(05)00741-3 fatcat:l5tz2ivssreuzg56qjcrhv7pkq

Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach

Matteo Polettini, Massimiliano Esposito
2013 Physical Review E  
We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time.  ...  Lett. 107, 010601 (2011)] regarding monotonicity of the large deviation rate functional for the occupation probability (dynamical activity), showing that while the conjecture might still hold in the long  ...  The research was supported by the National Research Fund Luxembourg in the frame of project FNR/A11/02.  ... 
doi:10.1103/physreve.88.012112 pmid:23944419 fatcat:54rgzlasmveshjfva2n3r3t32i

Violation of Local Detailed Balance Despite a Clear Time-Scale Separation [article]

David Hartich, Aljaž Godec
2022 arXiv   pre-print
Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee thermodynamic consistency arbitrarily far from equilibrium.  ...  Here we present a transparent example of a Markov model of a molecular motor where local detailed balance can be violated despite a clear time-scale separation and hence Markovian dynamics.  ...  In other words, time-scale separation may not suffice arbitrarily far from equilibrium.  ... 
arXiv:2111.14734v2 fatcat:iylot7kq6zhgdi3qhwvq72deqy

Lumping-Based Equivalences in Markovian Automata and Applications to Product-Form Analyses [chapter]

Andrea Marin, Sabina Rossi
2015 Lecture Notes in Computer Science  
The analysis of models specified with formalisms like Markovian process algebras or stochastic automata can be based on equivalence relations among the states.  ...  Quasi-reversibility is a pivotal property to study productform models, i.e., models whose equilibrium behaviour can be computed very efficiently without the problem of the state space explosion.  ...  In this paper we consider stochastic concurrent automata with an underlying continuous time Markov chain as common denominator of a wide set of Markovian stochastic process algebra.  ... 
doi:10.1007/978-3-319-22264-6_11 fatcat:a5tbtnomhjavlgxvxcmclocj3m

Process algebra for performance evaluation

Holger Hermanns, Ulrich Herzog, Joost-Pieter Katoen
2002 Theoretical Computer Science  
Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS).  ...  In total we consider four related calculi and investigate their relationship to existing Markovian process algebras.  ...  Acknowledgements The remarkable level of todays stochastic process algebra research has only been possible, since scientists of both communities, theoretical computer science and performance evaluation  ... 
doi:10.1016/s0304-3975(00)00305-4 fatcat:uab7q45gs5c43ixjzujjthe3dy

Foundations of Stochastic Thermodynamics [article]

Bernhard Altaner
2014 arXiv   pre-print
(ii) Markovian jump processes on finite state spaces are common models for bio-chemical pathways. How does one quantify and calculate fluctuations of physical observables in such models?  ...  Can one derive ST from an underlying reversible deterministic dynamics? Can we interpret ST's notions of entropy and entropy changes in a well-defined information-theoretical framework?  ...  In the limit of infinite time-scale separation these probabilities become time-independent and homogeneous and thus define the observable Markov process.  ... 
arXiv:1410.3983v1 fatcat:h3w4fxrfrjg55i4athygzfp5jy

Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems

Hong-Bin Chen, Guang-Yin Chen, Yueh-Nan Chen
2017 Physical Review A  
In the contest of quantity-based measures of non-Markovianity, the intuition of non-Markovianity in terms of information backflow is widely discussed.  ...  However, it is not easy to characterize the information flux for a given system state and show its connection to non-Markovianity.  ...  The system starts from a non-equilibrium initial state ρ(0) and evolves to another non-equilibrium state ρ(t) at a later time t. As shown in Refs.  ... 
doi:10.1103/physreva.96.062114 fatcat:txhi5owkrfaixj7o7loci6fkuy

Response time distributions and network perturbation into product-form

Peter G. Harrison, Maria G. Vigliotti
2009 Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools  
Response time calculations in stochastic networks are usually developed in terms of sample path analyses beginning in an equilibrium state.  ...  We consider the joint probability distribution of the sojourn times of a tagged task at each node of a path in a network and observe that this is the same in both the forward and reversed processes.  ...  , via joint sojourn time distributions and using reversed processes.  ... 
doi:10.4108/icst.valuetools2009.7776 dblp:conf/valuetools/HarrisonV09 fatcat:575utorwxzbqzbpndcmstl3ypq
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