Adiabatic index for relativistic stars as a coefficient of non-thermal dissipation

TL;DR

This paper demonstrates that the adiabatic index in relativistic stars functions as a non-thermal dissipation coefficient, linking stochastic pressure fluctuations to dissipation effects without heat flux, and introduces a formalism for stochastic effects in stellar interiors.

Contribution

It introduces a novel perspective on the adiabatic index as a dissipation constant and develops a formalism for stochastic effects in relativistic star interiors using a classical Einstein-Langevin approach.

Findings

Adiabatic index acts as a dissipation constant due to stochastic effects.

Pressure fluctuations are linked to dissipation without heat flux.

A fluctuation dissipation relation and Langevin fermi temperature are established.

Abstract

The adiabatic index of a relativistic star (modeled by a perfect fluid) is shown to act as a dissipation constant due to considerations of mesoscopic scale stochastic effects. This dissipative effect arises without taking heat flux in the fluid model and is termed as adiabatic or non-thermal for the system under consideration. A basic formalism for introducing stochastic effects in interiors of massive stars has recently been proposed via a classical Einstein-Langevin equation. The origin of stochasticity is associated with the pressure variable (due to degeneracy of constituent particles ) and its fluctuations,and is not viable for pressureless fluids. The fluctuations dissipate their fermi energy into perturbing the system, adiabatically. This is shown by a fluctuation dissipation relation, and a Langevin fermi temperature associated with these fluctuations is defined.The high magnitude of background field fluctuations which we get here, is feasible to account for perturbing the strong gravity regions with dense matter. Nevertheless, the perturbations themselves are consistently and reasonably small as first order deviations from equilibrium.