相关论文: Non-convergence to unstable equilibriums for conti…
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
We present an algorithm for finding the probabilities of rare events in nonequilibrium processes. The algorithm consists of evolving the system with a modified dynamics for which the required event occurs more frequently. By keeping track…
Nonequilibrium thermodynamics of a general second-order stochastic system is investigated. We prove that at steady state, under inversion of velocities, the condition of time-reversibility over the phase space is equivalent to the…
We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review…
The Fluctuation Theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy…
We discuss non-reversible Markov-chain Monte Carlo algorithms that, for particle systems, rigorously sample the positional Boltzmann distribution and that have faster than physical dynamics. These algorithms all feature a non-thermal…
We consider the dynamics of the charge carriers in a tunneling-enhanced percolation network, named as a Random Resistor cum Tunneling-bond Network (RRTN), where we allow tunneling in the gap between two randomly thrown nearest neighbour…
Robustness guarantees are important properties to be looked for during control design. They ensure stability of closed-loop systems in face of uncertainties, unmodeled effects and bounded disturbances. While the theory on robust stability…
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
This paper develops a time-inconsistent and path-dependent singular control framework incorporating a running minimum process. We derive a verification theorem that characterizes equilibria under substantially weaker regularity conditions…
Under many circumstances many soft and hard materials are present in a puzzling wealth of non-equilibrium amorphous states, whose properties are not stationary and depend on preparation. They are often summarized in unconventional "phase…
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…
We investigate the asymptotic behavior of sample functions of stable processes when $t{\to}\infty$. We compare our results with the iterated logarithm law, results for the first hitting time and most visited sites problems.
Non-equilibrium property of turbulence modifies characteristics of turbulent transport. With the aid of response-function formalism, such non-equilibrium effects in turbulent transport can be represented by the temporal variation of the…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…