Explain whether the following stereoisomers are inter-convertible (can be converted from one to the other) or not. Is there a specific name which is used to distinguish one from the other? Explain.

The following stereoisomers are not inter-convertible (cannot be converted from one to the other) because they are geometric isomers. The specific name used to distinguish them from one another is that the first one is trans-1,4-dimethylcyclopentane and the second one is cis-1,4-dimethylcyclopentane.
Stereoisomers are isomers with a similar structural formula but different spatial arrangements of substituent atoms or compounds. They can be subdivided into two groups, these are;
Conformational isomers are isomers that are not superimposable but readily interconvertible by rotation around single bonds. Examples of compounds that exhibit these forms of isomerism are:
Configurational isomers are stereoisomers that are not superimposable and non-interconvertible by rotation about the single bonds. An example of these types of isomers is geometric isomers.
Geometric isomerism often regarded as (cis-trans isomerism) is caused by the spatial geometry of their bond, which restricts rotation about it.
The physical characteristics of geometric isomers differ. As such, it is difficult to transform one geometric isomer to another.
The diagram given in the question is an example of Geometric isomers.
Therefore, we can conclude that since it is difficult to rotate about their single bonds in cis-trans isomers, the given stereoisomers are not inter-convertible.
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