Related papers: Beyond Linear Response: Equivalence between Thermo…
We adopt a geometric approach to describe the performance of adiabatic quantum machines, operating under slow time-dependent driving and in contact to two or more reservoirs with a temperature bias during all the cycle. We show that the…
Understanding heat transport in low-dimensional and nano-architectured materials remains a central challenge in nonequilibrium statistical physics due to persistent deviations from Fourier's law. These deviations are driven by…
In this paper the optimal transport and the metamorphosis perspectives are combined. For a pair of given input images geodesic paths in the space of images are defined as minimizers of a resulting path energy. To this end, the underlying…
Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…
We establish a finite-time quantum tricycle driven by an external field and investigate its thermodynamic performance in the slow-driving regime. By developing a perturbative expansion of heat with respect to operation time, we capture the…
We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the…
A remarkable connection between optimal design and Monge transport was initiated in the years 1997 in the context of the minimal elastic compliance problem and where the euclidean metric cost was naturally involved. In this paper we present…
Classical regression models do not cover non-Euclidean data that reside in a general metric space, while the current literature on non-Euclidean regression by and large has focused on scenarios where either predictors or responses are…
In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form…
The development of efficient artificial nanodevices poses challenges which are of fundamental and technological nature. Recent progress has been made in the context of finite-time thermodynamics. A central question in finite-time…
In contrast to the classical concept of a Carnot engine that alternates contact between heat baths of different temperatures, naturally occurring processes usually harvest energy from anisotropy, being exposed simultaneously to chemical and…
Irreversible processes accomplished in a fixed time involve nonlinearly coupled flows of matter, energy, and information. Here, using entropy production as an example, we show how thermodynamic uncertainty relations and speed limits on…
The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding…
Asking for the optimal protocol of an external control parameter that minimizes the mean work required to drive a nano-scale system from one equilibrium state to another in finite time, Schmiedl and Seifert ({\it Phys. Rev. Lett.} {\bf 98},…
This work is a geometrical approach to the optimization problem motivated by transportation system management. First, an attempt has been made to furnish a comprehensive account of geometric programming based on the elementary Finsler…
We provide a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that we show is canonically available, given a choice of complement to the distribution. We also describe conditions…
Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for…
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…
We discuss the relevance of geometric concepts in the theory of stochastic differential equations for applications to the theory of non-equilibrium thermodynamics of small systems. In particular, we show how the Eells-Elworthy-Malliavin…
We study the thermodynamic cost associated with driving systems between different non-equilibrium steady states. In particular, we combine a linear-response framework for non-equilibrium Markov systems with Lagrangian techniques to minimize…