  Casimir entropy is an important aspect of casimir effect.In this paper,we
employ the path integral method to derive the total relation for casimir
entropy and internal energy of arbitrary shaped objects in the presence of
two,three and four dimensions scalar fields and electromagnetic field.We obtain
the casimir entropy and internal energy of two nanoribbon immersed in scalar
field and two nanospheres immersed in scalar field and electromagnetic
field.The casmir entropy of two nanospheres immersed in the electromagnetic
field in small interval of temperature variations,shown a different behavior.
