Cosmological Stealth fields and Non-Equilibrium thermodynamics
We investigate the connection between cosmological stealth scalar fields and non-equilibrium thermodynamics in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) background. We consider a non-minimally coupled scalar field whose energy-momentum tensor vanishes identically, allowing the field to evolve on a dissipative cosmological background without producing gravitational backreaction. We show that the stealth condition leads to a generalized Riccati equation for the scalar-field kinematics, where the dissipative pressure acts as a thermodynamic driving term. In terms of the variable $y=\dotϕ/(Hϕ)$, the system admits two thermodynamic branches: a stable attractor selected by entropy production and an unstable repeller. We also construct the corresponding phase-space structure in the $(y,ω_{\rm eff})$ plane and identify a near-critical regime associated with $ζ=1/4$. Finally, we reconstruct the stealth potential and present a bulk viscous realization in which irreversible entropy production drives the universe toward an asymptotic de Sitter state while the stealth field tracks the dissipative background. We further develop the linear scalar perturbations of the model and show that, although the stealth field is gravitationally invisible at the background level, its perturbation couples directly to the dissipative-pressure perturbation. This coupling provides a mechanism for distinguishing dissipative and non-dissipative sources that share the same background expansion history. Our results suggest that stealth fields can be interpreted as dynamically non-trivial thermodynamic trackers of non-equilibrium cosmological evolution.