Can we add different fields to instances of the same entity? I have a City entity with two fields (Title and Population), and I have created two instances of that entity.

Can I add different fields to these two instances?

Thank for you responses but I want different approach
Let me put my question in this way

1) I have entity:  City (with fields Population and Title)

2) of which I created two content (what should i call Chicago an New York ? contens of type City or anything else??):

Chicago and New York

3) now i know the entity City is fieldable i.e i can add custome fields to it, but those will be accesible to both ‘Chicago’ and ‘New York

4) What I want is ‘Chicago’ and ‘New York’ also be fieldable and have distinct field as well as common field

5) so, it should look like as
  Chicago : (Title - ‘Chicago’, Population - 1000, CField1 - ‘Hello’)
  New York: (Title - ‘Chicago’, Population - 1000, NField1 - ‘Hello’, NField2 - ‘Hello’)

Please tell me if above requirement is possible to implement
This single entity will use all of the fields you attach to it – it's still 1 instance (what we call a 'bundle') of an entity.

If you want to conditionally allow fields to be displayed on the entity edit form (or the display of the entity) use the Conditional Fields module: http://drupal.org/project/conditional_fields

If you really want to use different sets of fields, you need 2 different bundles, i.e. a "city" entity of bundle "foo" and a "city" entity of bundle "bar".