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We introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
We study an energy relaxation process after many degrees of freedom are excited in a Hamiltonian system with a large number of degrees of freedom. Bottlenecks of relaxation, where relaxations of the excited elements are drastically slowed…
We study the dynamics of entropy in a time dependent potential and explore how disorder influences this entropy flow. We show that disorder can trap entropy at the edge of the atomic cloud enabling a novel cooling method. We demonstrate the…
We have shown how the intrinsic properties of a noise process can set an upper bound for the time derivative of entropy in a nonequilibrium system. The interplay of dissipation and the properties of noise processes driving the dynamical…
We consider a body immersed in a perfect gas, moving under the action of a constant force E along the x axis . We assume the gas to be described by the mean-field approximation and interacting elastically with the body, we study the…
We study the transient response of a colloidal bead which is released from different heights and allowed to relax in the potential well of an optical trap. Depending on the initial potential energy, the system's time evolution shows…
Some dynamical properties of time-dependent driven elliptical-shaped billiard are studied. It was shown that for the conservative time-dependent dynamics the model exhibits the Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008)]. On…
Relaxation and correlation times are two parameters used frequently in approximate descriptions of the time development of hadronizing system from some initial state towards distributions observed experimentally. Chosen to reproduce the…
We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience…
A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features…
This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…
We study the energy flow of dissipative dynamics on infinite lattices, allowing the total energy to be infinite and considering formally gradient dynamics. We show that in spatial dimensions 1,2, the flow is for almost all times arbitrarily…
We investigate the old problem of the fast relaxation of collisionless $N$-body systems which are collapsing or perturbed, emphasizing the importance of (non-collisional) discreteness effects. We integrate orbit ensembles in fixed external…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
We investigate the time evolution of the entanglement entropy of coupled single-mode Bose-Einstein condensates in a double well potential at $T=0$ temperature, by combining numerical results with analytical approximations. We find that the…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing…
We study some aspects of equilibrium and off equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles N and study their scaling behavior with…