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Is there a mathematical proof for why a reversible process is one that has many infinitesimal equilibrium steps, rather than fewer large steps?

Maybe something along the lines of this?:

\begin{equation} \lim_{\Delta\rightarrow0}[f(\Delta,r,....)]=0 \end{equation}

where $\Delta$ is the step size, $r$ the distance and $f$ the energy loss of the system.

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