Casimir ‎effects‎‎ of nano objects in fluctuating scalar and electromagnetic fields: Thermodynamic investigating

 Casimir entropy is an important aspect of casimir effect and at the nanoscale is visible. In this paper, we employ the path integral method to ‎obtain a‎ ‎general‎ relation for casimir entropy and ‎i‎nternal energy of arbitrary shaped objects in the presence of two, three and four dimension scalar fields and ‎the‎ electromagnetic field. For this purpose, using Lagrangian and based on a perturbative approach, a series expansion in susceptibility function of the medium was obtained for the Casimir force between arbitrary shaped objects foliated in a scalar or vector fluctuating field in arbitrary dimensions. The finite temperature corrections are derived and using it, we obtain the casimir entropy and internal energy of two nano ‎rib‎bons immersed in the scalar field and two nanospheres immersed in the scalar field and the electromagnetic field. The casimir entropy of two nanospheres immersed in the electromagnetic field ‎behave ‎differently‎ in small interval of temperature variations.  .