  In this paper, we obtain the law of emergence with Tsallis entropy from the
thermodynamic laws. We first derive the law of emergence from the equilibrium
description of the unified first law and Clausius relation. However, it has
been shown that considering Tsallis entropy as the horizon entropy, the
Clausius relation $\delta Q=T dS$ does not hold due to non-equilibrium
thermodynamics and is replaced by the entropy-balance relation $dS=\frac{\delta
Q}{T}+d_{i}S$, where $d_iS$ is the additional entropy produced due to the
irreversible thermodynamic process. Hence, we derive the law of emergence from
the non-equilibrium description of thermodynamic laws. The comparison between
the law of emergence in both cases shows that the law of emergence from the
non-equilibrium approach describes the expansion of the universe in terms of
the areal volume, unlike the effective volume in the equilibrium case. We have
further shown that the law of emergence also satisfies the condition of the
maximization of entropy for a de Sitter universe; thus, the entropy of the
universe evolves to a bounded value in the asymptotic future.
