Exploring transitions of space plasmas out of equilibrium

Space plasmas from the solar wind to planetary magnetospheres and the outer heliosphere are systems in stationary states out of equilibrium. Empirical kappa distributions, which naturally emerge from Tsallis Statistics, successfully describe these space plasmas. The Tsallis formalism offers a solid statistical foundation and provides a set of proven tools for understanding these distributions, including a consistent definition of temperature - the physical temperature, which characterizes the non-equilibrium stationary states. Here, we develop a measure of the "thermodynamic distance" of stationary states away from equilibrium. The stationary states are labeled by the value of the entropic q-index, lying in a spectrum from q = 1 (equilibrium) to the maximum value of q, which specifies the furthest possible stationary state from equilibrium. We call this the "q-frozen state," because as a system approaches this state, it behaves analogously to when its temperature approaches absolute zero. We also introduce a novel isothermal procedure that describes a system's transition into different stationary states by varying the q-index, and show how the variation of temperature can be realized using an "iso-metastability" procedure, in which the system remains in a fixed stationary state. These innovations allow a generalization of the zeroth law of thermodynamics to cover stationary states out of equilibrium. By expressing the entropy in terms of the q-index, we show the detailed paths by which the transition of stationary states evolves toward equilibrium following the dynamics of a characteristic difference equation along the q-indices. This naturally exhibits certain stationary states out of equilibrium that are frequently observed in space plasmas.