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All the laws of physics are time-reversible. Time arrow emerges only when ensembles of classical particles are treated probabilistically, outside of physics laws, and the entropy and the second law of thermodynamics are introduced. In…
In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics, first and foremost because quantum measurements are invasive. Going beyond measurement invasiveness, here we…
We consider the dynamics of a continuously monitored qubit in the limit of strong measurement rate where the quantum trajectory is described by a stochastic master equation with Poisson noise. Such limits are expected to give rise to…
We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
The thermodynamic behavior of Markovian open quantum systems can be described at the level of fluctuations by using continuous monitoring approaches. However, practical applications require assessing imperfect detection schemes, where the…
Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…
It is shown that the exact dynamics of a composite quantum system can be represented through a pair of product states which evolve according to a Markovian random jump process. This representation is used to design a general Monte Carlo…
Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have…
We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator…
We consider quantum trajectories arising from disordered, repeated generalized measurements, which have the structure of Markov chains in random environments (MCRE) with dynamically-defined transition probabilities; we call these disordered…
We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation,…
The physics of Markovian open quantum systems can be described by quantum master equations. These are dynamical equations, that incorporate the Hamiltonian and jump operators, and generate the system's time evolution. Reconstructing the…
The large deviation theory has recently been applied to open quantum systems to uncover dynamical crossovers in the space of quantum trajectories associated to Markovian evolutions. Such dynamical crossovers are characterized by qualitative…
The state matrix $\rho$ for an open quantum system with Markovian evolution obeys a master equation. The master equation evolution can be unraveled into stochastic nonlinear trajectories for a pure state $P$, such that on average $P$…
We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle,…
We consider a particle moving in continuous time as a Markov jump process; its discrete chain is given by an ordinary random walk on ${\mathbb Z}^d$ , and its jump rate at $({\mathbf x},t)$ is given by a fixed function $\varphi$ of the…
Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We…