Reversible thermodynamic process record

Let $P=(I_P,x_P^{-},x_P^{+},z_P,{\kappa }_P,r_P)$ be an admitted closed process record as defined in Thermodynamic process records and transfer conventions, with equilibrium endpoints $x_P^{-},x_P^{+}\in D_c$. The record is reversible relative to its declared boundary and protocol when the model also admits a reverse record $P^{\mathrm{r}\mathrm{e}\mathrm{v}}$ for the same system and material constitution, starting at $x_P^{+}$ and ending at $x_P^{-}$, such that every auxiliary and device state specified by the protocol is restored to its initial state and every signed boundary transfer is reversed. In particular,

$Q[P^{\mathrm{r}\mathrm{e}\mathrm{v}}]=-Q[P],W_{\mathrm{o}\mathrm{n}}[P^{\mathrm{r}\mathrm{e}\mathrm{v}}]=-W_{\mathrm{o}\mathrm{n}}[P]\mathrm{.}$

If the protocol records additional transfer channels, their signed values must likewise be negatives of their forward values. A record that is slow is not reversible merely because it is slow; it must satisfy the reverse-record condition above. Reversibility is therefore relative to what the model includes inside the boundary and which reverse controls it admits.