If you couple your system to a heat path that is at rest wrt a specific Lorentz frame, you of course lose Lorentz incariance. On the other hand the lagrangian o

If you couple your system to a heat path that is at rest wrt a specific Lorentz frame, you of course lose Lorentz incariance. On the other hand the lagrangian of the standard model itself is to my knowledge fully Lorentz invariant.