Thermal Casimir effect in κ-Minkowski space-time

We study the finite temperature Casimir effect for parallel plates in the κ -Minkowski space-time. Using the Matsubara formalism and imposing the Dirichlet boundary conditions on a massless κ -scalar field, we compute the κ -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 κ -deformed space-time. Our analysis yields an upper bound on the deformation parameter as a ≤ 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 ≤ 10 − 12 . We also obtain the expression for Stefan-Boltzmann’s law in κ -Minkowski space-time.