The Thermodynamics for Relativistic Multi-Fluid Systems
Abstract
This article extends the single-fluid relativistic irreversible thermodynamics theory of M\"uller, Israel and 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 real-part of this universe will notice that their knowledge of the universe parametrized using real, rather than 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 real universe.