Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration

TL;DR

This paper investigates quantum-induced corrections to the stress-energy tensor in thermodynamic equilibrium states with acceleration and vorticity, revealing new coefficients and effects on thermodynamic relations, especially for scalar fields at high acceleration.

Contribution

It identifies additional second-order quantum corrections to the stress-energy tensor in accelerating and rotating equilibrium states, expanding previous models and showing their impact on thermodynamic functions.

Findings

Additional second-order coefficients depend on stress-energy correlators.

Acceleration and vorticity modify the equation of state.

Corrections increase significantly for massive scalar fields at high acceleration.

Abstract

We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with non-vanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between \rho and p, that is the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field -- both massive and massless -- and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these non-ideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensor of the scalar field -- canonical or improved -- are thermodynamically inequivalent.