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The aim of this article is to analyze the relation between the second
thermodynamics and the arrow of time. For this purpose, a number of different
aspects in this so-called arrow of time are distinguished, in particular
those of time-(a)symmetry and of (ir)reversibility. Next I review
versions of the second law in the work of Carnot, Clausius,
Kelvin, Planck, Gibbs, Carath\'eodory and Lieb and Yngvason, and
investigate their connection with these aspects of the arrow of time.
It is shown that this connection varies a great deal along with these
formulations of the second law. According to the famous formulation by
Planck, the second law expresses the irreversibility of natural processes.
But in many other formulations irreversibility or even time-asymmetry
plays no role.
I therefore argue for the position that the second law has nothing to do
with the arrow of time.