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Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and…
In this paper we develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The new method relies on estimating conditional…
We consider a high-dimensional random constrained optimization problem in which a set of binary variables is subjected to a linear system of equations. The cost function is a simple linear cost, measuring the Hamming distance with respect…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
Motivated by wide-ranging applications such as video delivery over networks using Multiple Description Codes, congestion control, and inventory management, we study the state-tracking of a Markovian random process with a known transition…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
We model the stock price dynamics through a semi-Markov process obtained using a Poisson random measure. We establish the existence and uniqueness of the classical solution of a non-homogeneous terminal value problem and we show that the…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on…
This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…
The ongoing rapid urbanization phenomena make the understanding of the evolution of urban environments of utmost importance to improve the well-being and steer societies towards better futures. Many studies have focused on the emerging…
We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems. By applying the minimal dissipation principle, we uniquely isolate the coherent contribution to…
We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a…