the lower limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas

Absolute zero – is the lower limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as 0.

The coldest theoretically possible temperature

The coldest theoretically possible temperature is absolute zero, which is 0 K on the Kelvin scale, a thermodynamic temperature scale, and −273.15 °C on the Celsius scale.

the lowest conceivable temperature

Melvyn Bragg and his guests discuss absolute zero, the lowest conceivable temperature.

as 0 K

Absolute zero, defined as 0 K, is exactly equal to −273.15 °C, or −459.67 °F.

where no more heat can be removed from a system

Absolute zero is defined as the point where no more heat can be removed from a system, according to the absolute or thermodynamic temperature scale.

as that temperature where all atomic thermal motion ceases

This is, in fact, why absolute zero is defined as that temperature where all atomic thermal motion ceases.