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Separable equilibrium state probabilities via time reversal in Markovian process algebra

2005
*
Theoretical Computer Science
*

The

doi:10.1016/j.tcs.2005.08.007
fatcat:flbctbypmjbc3gtqxhkcuicmca
*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 ...##
###
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?

2009
*
Computer journal
*

The joint

doi:10.1093/comjnl/bxp021
fatcat:clyc2mxjtbfinjqllyq4nifxsa
*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*. ...##
###
Exploiting Quasi-reversible Structures in Markovian Process Algebra Models

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. ...

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

2014
*
arXiv
*
pre-print

., 1996] to generate

arXiv:1210.3094v2
fatcat:k32g2nojwncspfxy2or4xxoxw4
*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 ...##
###
Simultaneous Computation of Dynamical and Equilibrium Information Using a Weighted Ensemble of Trajectories

2014
*
Journal of Chemical Theory and Computation
*

We also describe a related history-dependent matrix procedure for estimating

doi:10.1021/ct401065r
pmid:25246856
pmcid:PMC4168800
fatcat:bp7ygcwcxfbw3pt4h7k7cis4ge
*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*. ...##
###
Process Algebraic Non-product-forms

2006
*
Electronical Notes in Theoretical Computer Science
*

A generalization of the

doi:10.1016/j.entcs.2006.03.012
fatcat:uyf5ikzm5jau7kbcpi4gk5v764
*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 ...##
###
Author index

2005
*
Theoretical Computer Science
*

Lee,

doi:10.1016/s0304-3975(05)00741-3
fatcat:l5tz2ivssreuzg56qjcrhv7pkq
*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. ...##
###
Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach

2013
*
Physical Review E
*

We show

doi:10.1103/physreve.88.012112
pmid:23944419
fatcat:54rgzlasmveshjfva2n3r3t32i
*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. ...##
###
Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
[article]

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*. ...

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

2015
*
Lecture Notes in Computer Science
*

The analysis of models specified with formalisms like

doi:10.1007/978-3-319-22264-6_11
fatcat:a5tbtnomhjavlgxvxcmclocj3m
*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*. ...##
###
Process algebra for performance evaluation

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 ...

##
###
Foundations of Stochastic Thermodynamics
[article]

2014
*
arXiv
*
pre-print

(ii)

arXiv:1410.3983v1
fatcat:h3w4fxrfrjg55i4athygzfp5jy
*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*. ...##
###
Thermodynamic description of non-Markovian information flux of nonequilibrium open quantum systems

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. ...

##
###
Response time distributions and network perturbation into product-form

2009
*
Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools
*

Response

doi:10.4108/icst.valuetools2009.7776
dblp:conf/valuetools/HarrisonV09
fatcat:575utorwxzbqzbpndcmstl3ypq
*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*. ...
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