Related papers: Beyond Linear Response: Equivalence between Thermo…
A quadratic optimal transport metric on the set of probability measure over $\R^2$ is introduced. The quadratic cost is given by the euclidean norm on $\R^2$ associated to some well chosen symmetric positive matrix, which makes the metric…
Efficient control schemes that enable fast, high-fidelity operations are essential for any practical quantum computation. However, current optimization protocols are intractable due to stringent requirements imposed by the microscopic…
For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to…
We derive a geometrical expression of the excess entropy production for quasi-static transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The…
Thermodynamic computing exploits fluctuations and dissipation in physical systems to efficiently solve various mathematical problems. For example, it was recently shown that certain linear algebra problems can be solved thermodynamically,…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…
We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it…
Linear response theory serves as a fundamental tool in the study of quantum transport, extensively employed to elucidate fundamental mechanisms related to the nature of the particles involved and the underlying symmetries. This framework…
Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…
In these lecture notes, partly based on a course taught at the Karpacz Winter School in March 2014, we explore the close connections between non-adiabatic response of a system with respect to macroscopic parameters and the geometry of…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject…
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…
Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to…
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher's Information Matrix. In this work we…
In this letter, we first redefine our formalism of the thermodynamic geometry introduced in [1,2] by changing coordinates of the thermodynamic space by means of Jacobian matrices. We then show that the geometrothermodynamics (GTD) is…
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry…
Local thermal equilibrium generally implies the absence of heat flux within a fluid. We find the relations between a set of thermodynamic variables of a fluid on a general spacetime and those defined on a conformally connected spacetime,…