Finite temperature effective potential and its qubit interpretation

Abstract In this work, we demonstrate that the finite temperature effective potential for a free quantum field theory can be expressed in terms of the Von Neumann entropy derived from a pseudo-Hermitian qubit density matrix associated with the differential operator involved—in the present description the Dirac operator. This paper broadens the previous formalism established for the Casimir effect by incorporating finite temperature considerations without imposing any assumptions on the boundary conditions or the spectrum, aside from ensuring the self-adjointness of the problem. The established relationship between the zero-temperature vacuum energy and the Von Neumann entropy maintains a consistent form, while introducing finite temperature enables us to articulate the connection between the finite temperature effective potential and total entropy (comprising both thermodynamic and Von Neumann entropies) in a manner reminiscent of a generalized first law of thermodynamics. We prove that the von Neumann entropy of qubit degrees of freedom of virtual particles is extremised.