Carnot established in 1824 that the efficiency of cyclic engines operating between a hot bath at absolute temperature Thot and a cold bath at temperature Tcold cannot exceed 1−Tcold/Thot. This result implies the existence of an entropy function S(U) with the property that dS/dU ≤ 0, where U denotes the average energy. Linear singlemode systems alternately in contact with hot and cold baths obey...

Given a family of vector fields we introduce a notion of convexity and of semiconvexity of a function along the trajectories of the fields and give infinitesimal characterizations in terms of inequalities in viscosity sense for the matrix of second derivatives with respect to the fields. We also prove that such functions are Lipschitz continuous with respect to the Carnot-Carathéodory distance ...

We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discret...

This paper describes the application of stochastic grey-box modeling to identify electrical power consumption-to-temperature models of a domestic freezer using experimental measurements. The models are formulated using stochastic differential equations (SDEs), estimated by maximum likelihood estimation (MLE), validated through the model residuals analysis and cross-validated to detect model ove...

Large amounts of waste heat, below 120 °C, are released globally by industry. To convert this low-temperature heat to power, thermally regenerative flow batteries have recently been studied. Most analyses focused on either the discharging or regeneration phase. However, both phases be considered in order holistically assess performance battery. Therefore, a dynamic, open-access, full-cycle mode...

The order of growth of a harmonic function is determined by the growth of its gradient and conversely. We extend these results to solutions of certain subelliptic equations in John domains in Carnot groups. The modulus of the gradient is replaced by a local average of the horizontal gradient. In the harmonic case these quantities are equivalent. The proof uses recent integral inequalities assoc...