# The Thermodynamics for Relativistic Multi-Fluid Systems

## TL;DR

This paper extends relativistic thermodynamics to multi-fluid systems with species interactions, revealing that observers limited to real quantities may infer negative energies affecting cosmic expansion.

## Contribution

It introduces a multi-fluid thermodynamics framework with complex velocities, expanding the MIS theory to account for inter-species interactions.

## Key findings

- Multi-fluid thermodynamics with complex velocities.
- Observers see negative energy effects in the real universe.
- Inability of real quantities alone to fully describe the system.

## 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.