Steady-State Relative Differential Norm report a nan if using empty aux-system for steady state detection

[GiudGiud]

Reason

See discussion

How to Reproduce

See title Empty aux system check_aux = true in executioner

Impact

Very minor, no error and user will figure it out most likely The user sort of put themselves in the situation with check_aux and no aux-system

Discussed in https://github.com/idaholab/moose/discussions/27642

^{Originally posted by xu7875 May 16, 2024}

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Question

Hello MOOSE community,

I have a question on detecting steady state.

I got a report "Steady-State Relative Differential Norm: -nan" from my solve. However, my solve converges well.

After several time steps, my nonlinear residual already drops below my set tolerance, which means the my system does not evolve anymore. However, Steady-State Relative Differential Norm: -nan.

My question is how come such on one hand, it converges, on the other hand, Steady-State Relative Differential Norm: -nan?

Thank you,

Jiangang