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We study Markovian stochastic motion on a graph with finite number of nodes and adiabatically periodically driven transition rates. We show that, under general conditions, the quantized currents that appear at low temperatures are a…

Driven Langevin processes have appeared in a variety of fields due to the relevance of natural phenomena having both deterministic and stochastic effects. The stochastic currents and fluxes in these systems provide a convenient set of…

We give a new approach to the study of statistical mechanical systems: algebraic topology is used to investigate the statistical distributions of stochastic currents generated in graphs. In the adiabatic and low temperature limits we will…

We propose a highly-scalable method to compute the statistics of charge transfer in driven conductors. The framework can be applied in situations of non-zero temperature, strong coupling to terminals and in the presence of non-periodic…

Stochastic Thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from anti-symmetric jump observables defined on the edges of the graph representing the…

Small nonequilibrium systems in contact with a heat bath can be analyzed with the framework of stochastic thermodynamics. In such systems, fluctuations, which are not negligible, follow universal relations such as the fluctuation theorem.…

Current fluctuations play an important role in non-equilibrium statistical mechanics, and are a key object of interest in both theoretical studies and in practical applications. So far, most of the studies were devoted to the fluctuations…

We use algebraic topology to study the stochastic mo- tion of cellular cycles in a finite CW complex. Inspired by statis- tical mechanics, we introduce a homological observable called the average current. The latter measures the average…

A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…

We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of…

We demonstrate that the counting statistics of currents in periodically driven ergodic stochastic systems can show sharp changes of some of its properties in response to continuous changes of the driving protocol. To describe this effect,…

The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…

We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hardcore repulsion on a finite one-dimensional…

Continuous-time Markov chains have been successful in modelling systems across numerous fields, with currents being fundamental entities that describe the flows of energy, particles, individuals, chemical species, information, or other…

We study micromotion in two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized time-averaged magnetization density when the system…

We develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states. This theory is applied to a dichotomically driven Markovian two state…

We show that the fraction of time a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by L\'evy for Brownian motion. Stochastic currents with long streaks above or below their average…

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from…

The exact stochastic decomposition of non-Markovian dissipative quantum dynamics is combined with the time-dependent semiclassical initial value formalism. It is shown that even in the challenging regime of moderate friction and low…

When parameters are varied periodically, charge can be pumped through a mesoscopic conductor without applied bias. Here, we consider the inverse effect in which a transport current drives a periodic variation of an adiabatic degree of…