Newton's cooling law in generalised statistical mechanics

The study of cooling materials is essential to analyse the thermal properties of substances, electronic devices, among many others. The physical law for describing the temporal temperature decrease has been dominated by Newton's law of cooling (NLC), which assumes that the natural cooling occurs by following an exact exponential trend. However, several studies have questioned the broad validity of this law by arguing that cooling occurs following an approximate rather than an exact exponential trend. In this way, to mitigate the difficulties of a reliable-description of the natural cooling processes, we introduce in this work a new formulation of NLC in the context of the q- and kappa-calculus, which are obtained from the Tsallis q- and Kaniadakis kappa-generalised statistical mechanics. The NLC in the Tsallis and Kaniadakis frameworks, in which we call q-NLC and kappa-NLC, respectively, are derived from the related deformed derivative operators. The q- and kappa-NLC describes the cooling process through the deformation of the ordinary exponential function. To empirically validate our proposal, we consider two real data sets: in the first one, a water-cooling case-study; and then, in the second one, the cooling of a power battery pack. The results show that the NLC based on generalised statistics outperform the classical NLC, which demonstrates a new path to cooling-analyses. (C) 2020 Elsevier B.V. All rights reserved.