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Total entropy generated by the Unruh effect is calculated within the framework of information theory. In contrast to previous studies, here the calculations are done for the finite time of existence of the non-inertial reference frame. In this case only the finite number of particles is produced. Dependence on mass of the emitted particles is taken into account. Analytic expression for the entropy of radiated boson and fermion spectra is derived. We study also its asymptotics corresponding to limiting cases of low and high acceleration. The obtained results can be further generalized to other intrinsic degrees of freedom of the emitted particles, such as spin and electric charge.
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We present a general method to determine the entropy current of relativistic matter at local thermodynamic equilibrium in quantum statistical mechanics. Provided that the local equilibrium operator is bounded from below and its lowest lying eigenvector is non-degenerate, it is proved that, in general, the logarithm of the partition function is extensive, meaning that it can be expressed as the integral over a 3D space-like hypersurface of a vector current, and that an entropy current exists. We work out a specific calculation for a non-trivial case of global thermodynamic equilibrium, namely a system with constant comoving acceleration, whose limiting temperature is the Unruh temperature. We show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy.
We propose a test for the circular Unruh effect using certain atoms - fluorine and oxygen. For these atoms the centripetal acceleration of the outer shell electrons implies an effective Unruh temperature in the range 1000 - 2000 K. This range of Unruh temperatures is large enough to shift the expected occupancy of the lowest energy level and nearby energy levels. In effect the Unruh temperature changes the expected pure ground state, with all the electrons in the lowest energy level, to a mixed state with some larger than expected occupancy of states near to the lowest energy level. Examining these atoms at low background temperatures and finding a larger than expected number of electrons in low lying excited levels, beyond what is expected due to the background thermal excitation, would provide experimental evidence for the Unruh effect.
When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by E. Verlindes paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.
We address the validity of the single-mode approximation that is commonly invoked in the analysis of entanglement in non-inertial frames and in other relativistic quantum information scenarios. We show that the single-mode approximation is not valid for arbitrary states, finding corrections to previous studies beyond such approximation in the bosonic and fermionic cases. We also exhibit a class of wave packets for which the single-mode approximation is justified subject to the peaking constraints set by an appropriate Fourier transform.
A detector undergoing a huge acceleration measures a thermal distribution with the Unruh temperature out of the Minkowski vacuum. Though such huge accelerations occur naturally in astrophysics and gravity, one may design untraintense laser facility to detect the Unruh effect and simulate laboratory astrophysics. We derive the QED vacuum polarization and the vacuum persistence amplitude as well as the Schwinger pair creation in an accelerating frame when a constant electric field exists in the Minkowski spacetime. We advance a thermal interpretation of Schwinger pair creation in the Rindler space.
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