Related papers: Open Markov Processes and Reaction Networks
Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative…
We study finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
We analyse diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have…
Suppose that $(X_t)_{t \ge 0}$ is a one-dimensional Brownian motion with negative drift $-\mu$. It is possible to make sense of conditioning this process to be in the state $0$ at an independent exponential random time and if we kill the…
We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the…
There are some positively divisible non-Markovian processes whose transition matrices satisfy the Chapman-Kolmogorov equation. These processes should also satisfy the Kolmogorov consistency conditions, an essential requirement for a process…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…
We study the Markovianity of a composite system and its subsystems. We show how the dissipative nature of a subsystem's dynamics can be modified without having to change properties of the composite system environment. By preparing different…
We consider a robust approach to address uncertainty in model parameters in Markov Decision Processes (MDPs), which are widely used to model dynamic optimization in many applications. Most prior works consider the case where the uncertainty…
We consider a branching system consisting of particles moving according to a Markov family in $\Rd$ and undergoing subcritical branching with a constant rate $V>0$. New particles immigrate to the system according to homogeneous space-time…
Current concepts of neural networks have emerged over two centuries of progress beginning with the neural doctrine to the idea of neural cell assemblies. Presently the model of neural networks involves distributed neural circuits of nodes,…
We investigate the total stochastic entropy production of a two-level bosonic open quantum system under protocols of time dependent coupling to a harmonic environment. These processes are intended to represent the measurement of a system…
Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond…