We study an homogenization problem for Hamilton-Jacobi equations in the geometry of Carnot Groups.The tiling and the corresponding notion of periodicity are compatible with the dilatations of the Group and use the Lie bracket generating property. 1. Background and motivations Consider a Hamilton-Jacobi equation: u+H(ξ,∇u) = 0 in R where the Hamiltonian H(ξ, p) : R × RN×N → R is not coercive in ...

Heat engines constitute the major building blocks of modern technologies. However, conventional heat with higher power yield lesser efficiency and vice versa respect various power-efficiency trade-off relations. This is also assumed to be true for operating in quantum regime. Here we show that these relations are not fundamental. We introduce deliver maximum Carnot one-shot finite-size These co...

Random noise can generate a unidirectional heat current across asymmetric nano-objects in the absence (or against) a temperature gradient. We present a minimal model for a molecular-level stochastic heat pump that may operate arbitrarily close to the Carnot efficiency. The model consists a fluctuating molecular unit coupled to two solids characterized by distinct phonon spectral properties. Hea...

Small amounts of useful power may be generated in polar or subpolar regions during the winter period by placing a heat engine between a large body of water (near PC), acting as a heat source, and the atmosphere (near -25OC), acting as a heat sink. The scheme consists of a fuelless modular system operating on the Carnot cycle. Power is extracted by a reciprocating vapour engine drawing saturated...

We show that the Heisenberg group, with its Carnot-Caratheodory metric, does not admit a bi-Lipschitz embedding into L1.

A thermodynamic formalism is developed for a system of interacting particles under overdamped motion, which has been recently analyzed within the framework of nonextensive statistical mechanics. It amounts to expressing the interaction energy of the system in terms of a temperature θ, conjugated to a generalized entropy s(q), with q = 2. Since θ assumes much higher values than those of typical ...

Carnot established in 1824 that the efficiency of cyclic engines operating between a hot bath at absolute temperature Thot and a bath at a lower temperature Tcold cannot exceed 1−Tcold/Thot. We show that linear oscillators alternately in contact with hot and cold baths obey this principle in the quantum as well as in the classical regime. The expression of the work performed is derived from a s...

Trevor I. Smith, Warren M. Christensen, Donald B. Mountcastle, and John R. Thompson Department of Physics and Astronomy and Department of STEAM Education, Rowan University, Glassboro, New Jersey 08028, USA Department of Physics and Astronomy, North Dakota State University, Fargo, North Dakota 58102, USA Department of Physics and Astronomy, University of Maine, Orono, Maine 04469, USA Maine Cent...