$A$	heat transfer area, ${\mathrm{m}}^2$
$C$	heat leakage coefficient, $W/K$
$CF$	correction factor
$D$	internal irreversibility
$g$	number of possible spin orientations of a gas particle
$h$	Planck’s constant, $J\cdot s$
$k$	Boltzmann’s constant, $J/K$
$L$	Lagrangian function
$m$	rest mass of a gas particle, $\mathrm{kg}$
$n$	number density of gas particles, ${1/\mathrm{m}}^3$
$N$	total number of particles
$P$	power output, $W$
$p$	gas pressure, $\mathrm{Pa}$
$Q$	amount of heat exchange, $J$
$\dot{Q}$	rate of heat flow, $W$
$S$	entropy, $J/K$
$t$	heat transfer time, $s$
$T$	temperature, $K$
$U$	internal energy, $J$
$V$	volume of gas, ${\mathrm{m}}^3$
$v$	average volume that an ideal quantum gas particle occupies, ${\mathrm{m}}^3$
$W$	work, $J$
${\rm Z}$	simplified factor
$z$	fugacity of gas
Greek Letters
$\alpha$	heat transfer coefficient, $W/\left({\mathrm{m}}^2\cdot K\right)$
$\varphi$	entropy ratio
$\Gamma$	gamma function
$\eta$	efficiency
$\mu$	chemical potential, $J$
$\tau$	cycle period, $s$
Subscripts
$B$	Bose gas
$F$	Fermi gas
$H$	hot side
$i$	heat leakage
$L$	cold side
$q$	ideal quantum gas
$0$	condensed state
$1,2,3,4$	cycle states
Superscripts
′	The irreversible process
Abbreviations
EMP	efficiency at the maximum power
HE	heat engine
MPO	maximum power output
QHE	quantum heat engine
WM	working medium