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We consider Markov Decision Processes (MDPs) in which every stationary policy induces the same graph structure for the underlying Markov chain and further, the graph has the following property: if we replace each recurrent class by a node,…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime,…
Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive…
We numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
Living systems maintain or increase local order by working against the Second Law of Thermodynamics. Thermodynamic consistency is restored as they dissipate heat, thereby increasing the net entropy of their environment. Recently introduced…
In statistical physics, entropy is generally logarithm of probability. Therefore, if dynamics is decomposed by log, entropy production should be decomposed properly. In the present work, log-decomposition of dynamics is introduced. By which…
We study irreversible processes for nonlinear oscillators networks described by complex-valued Langevin equations that account for coupling to different thermo-chemical baths. Dissipation is introduced via non-Hermitian terms in the…
We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process…
This paper considers an infinite-horizon Markov decision process (MDP) that allows for general non-exponential discount functions, in both discrete and continuous time. Due to the inherent time inconsistency, we look for a randomized…
A necessary and sufficient condition is obtained for the existence of strong stationary times for ergodic one-dimensional diffusions, whatever the initial distribution. The strong stationary times are constructed through intertwinings with…
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…
The second law of thermodynamics states that entropy production cannot be negative. Recent developments concerning uncertainty relations in stochastic thermodynamics, such as thermodynamic uncertainty relations and speed limits, have…
We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…
The entropy production rate is a key quantity in non-equilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress towards its full grasping. By…
We propose a housekeeping/excess decomposition of entropy production for general nonlinear dynamics in a discrete space, including chemical reaction networks and discrete stochastic systems. We exploit the geometric structure of…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary…
Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…