Rails 5.1+

Use saved_change_to_published?:

class SomeModel < ActiveRecord::Base
  after_update :send_notification_after_change

  def send_notification_after_change
    Notification.send(…) if (saved_change_to_published? && self.published == true)
  end

end

Or if you prefer, saved_change_to_attribute?(:published).

Rails 3–5.1

Warning

This approach works through Rails 5.1 (but is deprecated in 5.1 and has breaking changes in 5.2). You can read about the change in this pull request.

In your after_update filter on the model you can use _changed? accessor. So for example:

class SomeModel < ActiveRecord::Base
  after_update :send_notification_after_change

  def send_notification_after_change
    Notification.send(...) if (self.published_changed? && self.published == true)
  end

end

It just works.