diff --git a/arraycontext/container/__init__.py b/arraycontext/container/__init__.py
index 9eb3c45cc9c95c479a05422c9646e0489b1f2dc5..23f980c86eb8c8e7fc8b9ad144112147d0a9d169 100644
--- a/arraycontext/container/__init__.py
+++ b/arraycontext/container/__init__.py
@@ -122,7 +122,10 @@ def serialize_container(ary: ArrayContainer) -> Iterable[Tuple[Any, Any]]:
     r"""Serialize the array container into an iterable over its components.
 
     The order of the components and their identifiers are entirely under
-    the control of the container class.
+    the control of the container class. However, the order is required to be
+    deterministic, i.e. two calls to :func:`serialize_container` on the same
+    array container should return an iterable with the components in the same
+    order.
 
     If *ary* is mutable, the serialization function is not required to ensure
     that the serialization result reflects the array state at the time of the