${\mathcal{L}}_1=-\frac{P_V{P}_{\xi }}{M_{\xi }}\frac{\partial }{\partial P_V}$	${\mathcal{L}}_2=(\mathrm{\Pi }-{\mathrm{\Pi }}_{\text{ext}})\frac{\partial }{\partial P_V}$
${\mathcal{L}}_3=\frac{P_V}{M_V}\frac{\partial }{\partial V}$	${\mathcal{L}}_4=\frac{P_{\eta }}{M_{\eta }}\frac{\partial }{\partial \eta }$
${\mathcal{L}}_5=\frac{P_{\xi }}{M_{\xi }}\frac{\partial }{\partial \xi }$	${\mathcal{L}}_6=\left(\frac{P_V^2}{M_V}-k_B{T}_{\text{ext}}\right)\frac{\partial }{\partial P_{\xi }}$
${\mathcal{L}}_7=-\frac{P_{\eta }}{M_{\eta }}{p}_{{\mu }_i}{\nabla }_{p_{\mu i}}$	${\mathcal{L}}_8=\left[F_{\mu i}+G_{\mu i}-\frac{m_{\mu i}}{M_{\mu }}{F}_{\mu }\right]{\nabla }_{p_{\mu i}}$
${\mathcal{L}}_9=-\left[\frac{P_{\eta }}{M_{\eta }}+\frac{P_V}{3V{M}_V}\right]P_{\mu }{\nabla }_{P_{\mu }}$	${\mathcal{L}}_{10}=F_{\mu }{\nabla }_{P_{\mu }}$
${\mathcal{L}}_{11}=g{k}_{\mathrm{B}}[T-T_{\text{ext}}]\frac{\partial }{\partial P_{\eta }}$	${\mathcal{L}}_{12}=\frac{P_V}{3V{M}_V}{R}_{\mu }{\nabla }_{R_{\mu }}$
${\mathcal{L}}_{13}=\frac{P_{\mu }}{M_{\mu }}{\nabla }_{R_{\mu }}$	${\mathcal{L}}_{14}=\frac{P_{\mu i}}{m_{\mu i}}{\nabla }_{r_{\mu i}}$
$\delta {\mathcal{L}}_1^{†}=\gamma \left(1+P_V\frac{\partial }{\partial P_V}+k_{\mathrm{B}}{T}_{\text{ext}}{M}_V\frac{{\partial }^2}{\partial P_V^2}\right)$	$\delta {\mathcal{L}}_2^{†}={\gamma }_{\eta }\left(1+P_V\frac{\partial }{\partial P_{\eta }}+k_{\mathrm{B}}{T}_{\text{ext}}{M}_{\eta }\frac{{\partial }^2}{\partial P_{\eta }^2}\right)$