Extensivity, entropy current, area law and Unruh effect

Abstract

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.

12 pages, 1 figure. Published version in Phys Rev D

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Cited by in corpus (5)

• Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field
• Unruh effect for fermions from the Zubarev density operator
• Flavor vacuum entanglement in boson mixing
• Transport coefficients of magnetized neutron star cores
• Entropy current in relativistic quantum statistical mechanics