This is a design choice of the class; you can change this by redefining (or patching \@ssect@ltx).
With the redefinition:
\documentclass[]{revtex4-1}
\makeatletter
\def\@ssect@ltx#1#2#3#4#5#6[#7]#8{%
\def\H@svsec{\phantomsection}%
\@tempskipa #5\relax
\@ifdim{\@tempskipa>\z@}{%
\begingroup
\interlinepenalty \@M
#6{%
\@ifundefined{@hangfroms@#1}{\@hang@froms}{\csname @hangfroms@#1\endcsname}%
{\hskip#3\relax\H@svsec}{#8}%
}%
\@@par
\endgroup
\@ifundefined{#1smark}{\@gobble}{\csname #1smark\endcsname}{#7}%
%\addcontentsline{toc}{#1}{\protect\numberline{}#8}%
}{%
\def\@svsechd{%
#6{%
\@ifundefined{@runin@tos@#1}{\@runin@tos}{\csname @runin@tos@#1\endcsname}%
{\hskip#3\relax\H@svsec}{#8}%
}%
\@ifundefined{#1smark}{\@gobble}{\csname #1smark\endcsname}{#7}%
\addcontentsline{toc}{#1}{\protect\numberline{}#8}%
}%
}%
\@xsect{#5}%
}%
\makeatother
\begin{document}
\tableofcontents
\section{Numbered section}
\section*{Unnumbered section}
\end{document}

With the patch:
\documentclass[]{revtex4-1}
\usepackage{xpatch}
\makeatletter
\patchcmd{\@ssect@ltx}
{\addcontentsline{toc}{#1}{\protect\numberline{}#8}}
{}
{}
{}
\makeatother
\begin{document}
\tableofcontents
\section{Numbered section}
\section*{Unnumbered section}
\end{document}
I did look at the REVTeX guides and other such documents, but couldn't find any mention of unnumbered sections in the TOC.
Thanks for your help.
– Jack Yates Apr 14 '14 at 15:56\patchcmd. Could you add explanation on how it works? Any chance you know how to write a patch for this answer to this somewhat similar question? – Zaus Apr 05 '22 at 20:08