As I understand the question, the problem is in the "label" of the arrow and how to do the "circle" with arrows. One way to do this is to play with the properties of chemmove
and the arrows.
For example:
\schemestart
\chemfig{First molecule}
\arrow{->[
\chemname[24pt]{\chemfig{N@{st1}ADH}}{\scriptsize \parbox[c]{40pt}{\centering ammonium formate}}
\hspace{0.5cm}
\chemname[24pt]{\chemfig{N@{en1}AD}}{\chemfig{CO_2}}
\chemmove{\draw[->,shorten <=5pt, shorten >=5pt](st1) .. controls +(+50:8mm) and +(+130:8mm)..(en1);}
\chemmove{\draw[->,shorten <=5pt, shorten >=5pt](en1) .. controls +(-130:8mm) and +(-50:8mm)..(st1);}
\chemmove{\draw[->,shorten <=5pt, shorten >=5pt,transform canvas={yshift=-32pt}](st1) .. controls +(+50:8mm) and +(+130:8mm)..(en1);}
]}[,2.4]
\chemfig{second molecule}
\schemestop
Note that maybe further adjusting of the spaces is required.
UPDATE: Document class book works fine.
\documentclass{book}
\usepackage{empheq}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{empheq}[left=\empheqlbrace]{align}
\mathit{Loss(P,Q)} &= - \frac{1}{N} \sum_{x}^{N} P(x)\times
\log(Q(x)) \times \alpha_{\mathit{coefficients}}\\
\nabla\times\overline{E}\notag
&= -\frac{\partial\overline{B}}{\partial t}-\bar J_{\text{mi}}
\end{empheq}
\end{document}
I stole the {\mathit{coefficients}
from @Zarko and replaced \bar
by \overline
because IMHO this looks better.
SECOND UPDATE: Your code had several option clashes. I think I solved all of them apart from those associated to babel and greek, which I never was able to run on my machine. For instance, you do not need definecolor in order to set the link etc. colors.
\documentclass{book}
%% packages
\usepackage{amsfonts,amssymb} % needed for math fonts
\usepackage{empheq, nccmath}
\usepackage{amsmath} % needed for command eqref
\usepackage{longtable}
\usepackage{lmodern}
\usepackage{xcolor}
\usepackage[unicode,
,colorlinks=true
,breaklinks
% ,greek
]{hyperref}
\usepackage{bookmark}
\hypersetup{
colorlinks=true,
linkcolor=blue,
citecolor=green!0.3!blue!0.9
urlcolor=red!0.3!blue!0.9}
%\usepackage[greek,english]{babel}
\usepackage{alphabeta}
%%%
% \usepackage{}
%\usepackage[utf8]{inputenc}
\usepackage{algpseudocode}
\usepackage{algorithm}
%\usepackage[hyphenbreaks]{breakurl} % benötigt für das Brechen von URLs in Literaturreferenzen, hyphenbreaks auch bei %links, die über eine Seite gehen (mit hyphenation).
% needed for creating hyperlinks in the document, the option colorlinks=true gets rid of the %awful %boxes, breaklinks breaks lonkg links (list of figures), and ngerman sets everything for german as %default hyperlinks %language
% \definecolor{c1}{rgb}{0,0,1} % blue
% \definecolor{c2}{rgb}{0,0.3,0.9} % light blue
% \definecolor{c3}{rgb}{0.3,0,0.9} % red blue
% \hypersetup{
% linkcolor={c1}, % internal links
% citecolor={c2}, % citations
% urlcolor={c3} % external links/urls
% }
%
\usepackage{alphabeta}
\usepackage[numbers, authoryear]{natbib} % needed for cite and abbrvnat bibliography style
\usepackage[nottoc]{tocbibind} % needed for displaying bibliography and other in the table of contents
\usepackage{graphicx} % needed for \includegraphics
\usepackage{bigstrut} % needed for the command \bigstrut
\usepackage{enumerate} % needed for some options in enumerate
% \newcommand\Mycite[1]{%
% \citeauthor{#1}~[\citeyear{#1}]}
%
\begin{document}
\begin{empheq}[left=\empheqlbrace]{align}
\mathit{Loss(P,Q)} = - \frac{1}{N} \sum_{x}^{N} P(x)\times log(Q(x)) \times \alpha_{coefficients}
\nabla\times\bar E &= -\frac{\partial\bar B}{\partial t}-\bar J_{\text{mi}}
\end{empheq}
\end{document}
\documentclass{book}
\usepackage{empheq}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{empheq}[left=\empheqlbrace]{align}
\mathit{Loss(P,Q)} &= - \frac{1}{N} \sum_{x}^{N} P(x)\times
\log(Q(x)) \times \alpha_{\mathit{coefficients}}\\
\nabla\times\overline{E}\notag
&= -\frac{\partial\overline{B}}{\partial t}-\bar J_{\text{mi}}
\end{empheq}
\end{document}
I did not massage the equation here because I'm afraid of @Zarko ;-)
Best Answer
The problem was because I was using an older version. In my case this was solved by updating from TexLive 2017 to 2018.