Thermal Casimir effect in $\hat{I}º$-Minkowski space-time

Abstract

We study the finite temperature Casimir effect for parallel plates in the $\hat{I}º$-Minkowski space-time. Using the Matsubara formalism and imposing the Dirichlet boundary conditions on a massless $\hat{I}º$-scalar field, we compute the $\hat{I}º$-deformed corrections to thermal Casimir free energy, pressure, entropy, and internal energy. Our results demonstrate that space-time non-commutativity enhances the attractive nature of the thermal Casimir force while preserving thermodynamic consistency; the system satisfies the Nernst theorem and laws of thermodynamics remain intact in $\hat{I}º$-deformed space-time. Our analysis yields an upper bound on the deformation parameter as $a\le 10^{-18}m$. Furthermore, our results indicate that non-commutative effects become experimentally observable in Casimir effect studies when the ratio of the non-commutative scale to plate separation satisfies $a/L\le 10^{-12}$. We also obtain the expression for Stefan-Boltzmann's law in $\hat{I}º$-Minkowski space-time.