Abstract
This article extends the single-fluid relativistic irreversible thermodynamics theory of {\it M{\"u}ller}, {\it Israel} and {\it Stewart} (hereafter the {MIS} theory) to a multi-fluid system with inherent species interactions. This is illustrated in a two-fluid toy-model where an effective complex 4-velocity plays the role of a primary dynamical parameter. We find that an observer who resides in the {\it real}-part of this universe will notice that their knowledge of the universe parametrized using {\it real}, rather than {\it imaginary}, quantities are insufficient to fully determine properties such as the total energy density, pressure or entropy, In fact, such an observer will deduce the existence of some negative energy that affects the expansion of their perceived {\it real} universe.
Highlights
The extended relativistic thermodynamics theory by Muller, Israel and Stewart developed in [1–4] has found wide application in scenarios where the material content under investigation that can be modelled using singlefluid approximation, whether the material is made of (1) one species or (2) several species whose properties are given by the average or the bulk behaviour
The anisotropic pressure is given by is the initial development of the concept only considered such averages for a system that was in equilibrium via statistical mechanics, the latter development extends the theory by incorporating aspects that allowed for the nonequilibrium thermodynamics via the kinetic theory
Our starting point is the construction of the effective 4-velocity uμ that is the resultant of the various fluid species velocities and which is defined by the Cauchy-Riemann equations for 4-dimensions [28]
Summary
The extended relativistic thermodynamics theory by Muller, Israel and Stewart developed in [1–4] has found wide application in scenarios where the material content under investigation that can be modelled using singlefluid approximation, whether the material is made of (1) one species or (2) several species whose properties are given by the average or the bulk behaviour. This treatment forms the foundation of most studies in relativistic non-equilibrium thermodynamics found in the literature for idealised fluids.
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