Duality relation between radiation thermodynamics and cosmic string loop thermodynamics

We discuss thermodynamics of electromagnetic radiation, with p=(1/3)ρ and ST3V, and of cosmic string loops, with p=-(1/3)ρ and ST-3V, where p stands for pressure, T temperature, ρ energy density, S entropy, and V volume. We write the thermodynamic formalisms under a common framework that illustrates their formal relationship and allows us to go from one to the other through a smooth transformation. From a microscopic perspective, these relations arise from the energy relations u(λ)=hc/λ for the photons of electromagnetic radiation, and u(l)=(c4/a2G)l for cosmic string loops, a being a numerical (dimensionless) constant and λ and l the radiation wavelength and the length of a loop; G, c, and h are the gravitational constant, the speed of light in vacuo, and the Planck constant, respectively. The corresponding thermodynamic behaviors are seen to be connected through a related thermal duality corresponding to the change of T by T*=Tc2/T, with Tc a reference temperature related to h, c, and G. © 2011 American Physical Society.