Recently, empirical kappa distribution, commonly used to describe non-equilibrium systems like space plasmas, has been connected with non-extensive statistical mechanics. Here we show how a consistent definition of the temperature and pressure is developed for stationary states out of thermal equilibrium, so that the familiar ideal gas state equation still holds. In addition to the classical triplet of temperature, pressure, and density, this generalization requires the kappa index as a fourth independent thermodynamic variable that characterizes the non-equilibrium stationary states. All four of these thermodynamic variables have key roles in describing the governing thermodynamical processes and transitions in space plasmas. We introduce a novel characterization of isothermal and isobaric processes that describe a system's transition into different stationary states by varying the kappa index. In addition, we show how the variation of temperature or/and pressure can occur through an "iso-q" process, in which the system remains in a fixed stationary state (fixed kappa index). These processes have been detected in the proton plasma in the inner heliosheath via specialized data analysis of energetic neutral atom (ENA) observations from Interstellar Boundary Explorer. In particular, we find that the temperature is highly correlated with (1) kappa, asymptotically related to isothermal (~1,000,000 K) and iso-q (κ ~ 1.7) processes; and (2) density, related to an isobaric process, which separates the "Ribbon," P ≈ 3.2 pdyn cm–2, from the globally distributed ENA flux, P ≈ 2 pdyn cm–2.
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