I am not sure, but if the manufacturer displays the effect in 8 Ohms, 4 Ohms, 2 Ohms and 1 Ohm, you can be sure it's up to the job. IMO most amps are not even up to 2 Ohm loads, and even fewer can work in 1 Ohm loads.

An amp that can work safely in a 1 OHm load is a welding machine more or less, and to be that, it has to deliver a huge amount of Amperes and be constructed in a very stable manner, regarding electricity.

I look forward to read other people's explanation here

What speakers are you driving? What is their nominal (average) impedance? There are a couple of speakers that will have a 1 ohm load (or below) at certain frequencies but NOT over the their full operating range. My Martin Logan CLS speakers are a prime example their impedance varies from 0.78 ohms to 16 ohms, they are rated at a nominal 4 ohms.

There is two different answers to your question.
The first is that you load your amplifier with a 1 ohm load and test it.
The second answer is what are you trying to do? Do you have a speaker setup that is really 1 ohm? Is it 1 advertised ohm? At what frequency is it 1 ohm? What is the bandwidth of its 1 ohm? What is its phase at its 1 ohm point?

I think the simple answer is that it is easy enough to do this in an arbitrary specific case given a schematic or an interior shot of the unit in question, however it is absolutely impossible to provide a completely generic guideline. Different amplifier topologies have radically different efficiencies and abilities to push current.

Take a hypothetical example of a class A amp rated at 50W peak into 8 ohms. To drive a 1 ohm load it has to be able to deliver 2^3=8 times the current, and therefore 8 times the power (=400W) into 1 ohm. If we assume, for the sake of argument, that it is 50% efficient it will need to draw 800W (0.8kW) from the mains. The balance of 400W will have to be dissipated as heat. So the amp will need a power supply capable of delivering 0.8 kW and heatsinking capable of dissipating 400 W, both of which should be apparent from a cursory ocular inspection! However none of the above would apply to a class D amp, etc.

I agree with both Keld and Sam:

1. Most amps capable of driving 1 ohm loads will look like an arc welding apparatus
2. Most speakers that dip that low only do so at one particular frequency. The famous exception is of course the Apogee Scintilla, which on its 1 ohm setting only breaks above 2 ohms above about 3 kHz. Back in the day these were almost always mated with meaty Krell or Levinson amps.

So how can Struts tell if an amp can drive a 1 ohm load?

By looking at the type and number of the output devices and working out their current delivery capability, looking at the power supply transformer(s) and capacitors and looking at the amount of heatsinking. I would not claim to be able to tell how well it might accomplish the task, i.e. how good it might sound, but I would be able to make a pretty good guess as to whether it would have a hope in hell, or whether it would just blow a fuse or end up in a fireball.

Go back and look at some of JA's speaker test reviews and study the graphs of the freq vs impedence charts.

You should also check the Mfg's recommend low impedence rating. Most amps can handle 3-4 ohms on occasion, but at 2 ohms current draw will be higher as will heat, which will shut the amp off, without damage, usually.

JA's reviews will take you to school.

Manufacturer's specs, to start with.

And, for more than that, keep your fire extinguisher handy and your wallet ready to pay for lots of repair bills.

(i.e. I wouldn't experiment with things like that, personally, without some statement from the manufacturer)

My words, almost exactly

I've been using "stat's" of one brand or another since the early eighties. I have used; Dyna MK-III's, Adcom GFA545 and 555, Hafler DH-200 and 220, Acoustat TNT-200, Krell KSA-50 and KSA-100, Conrad Johnson MV-75, Crown XLS 202 and 402 (recent buys) and others. I've tried other amps but the ones listed are ones I own or have owned. I once tried a receiver that belongs to a friend. After 10 minutes of reasonably loud volume it started smelling funny.
None of the amps ever exhibited any untoward behavior. Within their power limits they all worked just fine.
Speakers used inlude Quad ESL-57's, Martin Logan CLS's and Monolith's, Apogee Stage's (ribbons not ESL's) and Acoustat Spectra 22's, Model 3's and Model 1's.
I believe the Atmosphere amps are OTL tube amps. Trying them with some stats is something I've always wanted to do.