We study properties of functions convex with respect to a given family X of vector fields, a notion that appears natural in Carnot-Carathéodory metric spaces. We define a suitable subdifferential and show that a continuous function is X -convex if and only if such subdifferential is nonempty at every point. For vector fields of Carnot type we deduce from this property that a generalized Fenchel...

Graded nilpotent Lie groups, or Carnot Groups are to subRiemannian geometry as Euclidean spaces are to Riemannian geometry. They are the metric tangent cones for this geometry. Hoping that the analogy between subRiemannian and Riemannian geometry is a strong one, one might conjecture that the subRiemannian geodesic flow on any Carnot group is completely integrable. We prove this conjecture is f...

Abstract Ocean Thermal Energy Conversion (OTEC) is a renewable energy source in which produced by converting the heat stored sea or ocean thermal into valuable work, based on temperature difference between warm surface seawater and cold deep seawater. One of OTEC system requirements to have at minimum 20 °C within depth 1000 m below level. Recognizing importance optimum water temperature, sever...

Abstract We describe all Carnot algebras with growth vector (2, 3, 5, 6), their normal forms, an invariant that separates them, and a change of basis transforms such algebra into form. For each form, Casimir functions symplectic foliations on the Lie coalgebra are computed. An forms left-invariant 6)-distributions described. A classification, up to isometries, sub-Riemannian structures 6)-Carno...

In the absence of phonon contribution, a weakly coupled single orbital noninteracting quantum dot thermoelectric setup is known to operate reversibly as a Carnot engine. This reversible operation, however, occurs only in the ideal case of vanishing coupling to the contacts, wherein the transmission function is delta shaped, and under open-circuit conditions, where no electrical power is extract...

Abstract A novel trend in the theory of thermodynamic limits for energy convertors and traditional heat & mass exchangers is analysed where certain special controls called the Carnot control variables play a common role. In terms of these controls an expression for the lost work has the same form in irreversible energy convertors and in traditional processes of purely dissipative transport. For...

A unified optimization criterion for Carnot engines and refrigerators is proposed. It consists of maximizing the product of the heat absorbed by the working system times the efficiency per unit time of the device, either the engine or the refrigerator. This criterion can be applied to both low symmetric dissipation Carnot engines and refrigerators. For engines the criterion coincides with the m...

the mechanical aspect of entropy-exergy relationship, together with the thermal aspect usually consid-ered, leads to an extended formulation of physical exergy based on both maximum useful work and maximum useful heat that are the outcome of available energy of a thermodynamic system. this approach suggests that a mechanical entropy can be studied, in addition to the already used thermal entrop...