In the derivation of the thermodynamics of overdamped systems, one ignores the kinetic energy contribution since the velocity is a fast variable. In this paper, we show that the kinetic energy needs to be present in the calculation of the heat distribution to have a correct correspondence between the underdamped and overdamped cases, meaning that the velocity can not be fully ignored in the thermodynamics of these systems. We do this by investigating in detail the effect of the kinetic energy for three different systems: the harmonic potential, the logarithm potential, and an arbitrary non-isothermal process.
Bibliographical noteFunding Information:
This work is supported by the Brazilian agencies CAPES and FAPERJ. P.V.P. would like to thank FAPERJ for his current PhD fellowship. R.A. was partially supported by a PhD Fellowship from CAPES. This study was financed in part by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
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