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Newton’s cooling law in generalised statistical mechanics

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  • da Silva, Sérgio Luiz Eduardo Ferreira

Abstract

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 κ-calculus, which are obtained from the Tsallis q- and Kaniadakis κ-generalised statistical mechanics. The NLC in the Tsallis and Kaniadakis frameworks, in which we call q-NLC and κ-NLC, respectively, are derived from the related deformed derivative operators. The q- and κ-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.

Suggested Citation

  • da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    • Handle: RePEc:eee:phsmap:v:565:y:2021:i:c:s0378437120308372
    DOI: 10.1016/j.physa.2020.125539
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    References listed on IDEAS

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    1. Soares, Abner D. & Moura Jr., Newton J. & Ribeiro, Marcelo B., 2016. "Tsallis statistics in the income distribution of Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 158-171.
    2. da Silva, Sérgio Luiz Eduardo Ferreira & dos Santos Lima, Gustavo Zampier & de Araújo, João Medeiros & Corso, Gilberto, 2021. "Extensive and nonextensive statistics in seismic inversion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    3. Kaniadakis, G., 2006. "Towards a relativistic statistical theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 17-23.
    4. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    5. Oikonomou, Th. & Provata, A. & Tirnakli, U., 2008. "Nonextensive statistical approach to non-coding human DNA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2653-2659.
    6. da Silva, Sérgio Luiz Eduardo Ferreira & da Costa, Carlos A.N. & Carvalho, Pedro Tiago C. & de Araújo, João Medeiros & dos Santos Lucena, Liacir & Corso, Gilberto, 2020. "Robust full-waveform inversion using q-statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    7. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    8. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
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