  We derive the low temperature thermodynamic equations corrected by virtual
processes for integrable QFT on large but finite size space circle. Obtained
TBA's are solved numerically for the sinh-Gordon model. We also derive
corresponding Euler scale generalized hydrodynamic (GHD) equations and display
them explicitly for small occupation ratio of virtual quasiparticles. The
spectrum of velocities for the linear approximation to GHD is numerically
calculated.
