Related papers: Trajectory Convergence from Coordinate-wise Decrea…
We consider trajectories where the sign of the derivative of each entry is opposite to that of the corresponding entry in the gradient of an energy function. We show that this condition guarantees convergence when the energy function is…
We consider the minimization of a convex objective function subject to the set of minima of another convex function, under the assumption that both functions are twice continuously differentiable. We approach this optimization problem from…
For a fixed smooth map $u_0$ between two Riemann surfaces $\Sigma$ and $S$ with non-zero degree, we consider the energy function on Teichm\"uller space $\mc{T}$ of $\Sigma$ that assigns to a complex structure $t\in \mc{T}$ on $\Sigma$ the…
Concavity properties prevent the existence of significant landscapes in energy surfaces obtained by strict constrained energy minimizations. The inherent contradiction is due to fluctuations of collective coordinates. A solution to those…
Power systems are undergoing unprecedented transformations with the incorporation of larger amounts of renewable energy sources, distributed generation and demand response. All these changes, while potentially making power grids more…
A dynamical system is defined in terms of the gradient of a payoff function. Dynamical variables are of two types, ascent and descent. The ascent variables move in the direction of the gradient, while the descent variables move in the…
An analysis of one and two point functions of the energy momentum tensor on homogeneous spaces of constant curvature is undertaken. The possibility of proving a $c$-theorem in this framework is discussed, in particular in relation to the…
We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimisers are convex in dimension two. This positively answers an…
Energy transport can reveal information about interacting many-body systems beyond other transport probes. In particular, in one dimension it has been shown that the energy current is directly proportional to the central charge, thus…
We consider a reinforcement learning framework where agents have to navigate from start states to goal states. We prove convergence of a cycle-detection learning algorithm on a class of tasks that we call reducible. Reducible tasks have an…
We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…
Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow…
It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energy-diminishing methods to preserve…
Time-reversal symmetry of most conservative forces constrains the properties of linear transport in most physical systems. Here, I study the efficiency of energy transfer in oscillator networks where time-reversal symmetry is broken locally…
A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a…
Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is…
We prove the weak and the strong convergence of the trajectories of the continuous gradient projection method under some mild assumptions on the objective function and the step size function. Moreover, we estimate the decay rate to…
The analytical background of nonlinear observers based on minimal energy estimation is discussed. It is shown that locally the derivation of the observer equation based on a trajectory with pointwise minimal energy can be done rigorously.…
Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…