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.