diff --git a/datafusion/physical-expr/src/aggregate.rs b/datafusion/physical-expr/src/aggregate.rs
index 2e82ab2ab263..0fe08729828c 100644
--- a/datafusion/physical-expr/src/aggregate.rs
+++ b/datafusion/physical-expr/src/aggregate.rs
@@ -548,8 +548,9 @@ impl AggregateFunctionExpr {
     }
 
     /// Returns PhysicalSortExpr based on monotonicity of the function
-    pub fn natural_sort_expr(&self, aggr_func_idx: usize) -> Option<PhysicalSortExpr> {
-        // If the aggregate expressions are set-monotonic, the output data is naturally ordered with it.
+    pub fn get_result_ordering(&self, aggr_func_idx: usize) -> Option<PhysicalSortExpr> {
+        // If the aggregate expressions are set-monotonic, the output data is
+        // naturally ordered with it per group or partition.
         let monotonicity = self.set_monotonicity();
         if !monotonicity.is_monotonic() {
             return None;
diff --git a/datafusion/physical-expr/src/window/aggregate.rs b/datafusion/physical-expr/src/window/aggregate.rs
index f22c693126bc..d94cdc1490dd 100644
--- a/datafusion/physical-expr/src/window/aggregate.rs
+++ b/datafusion/physical-expr/src/window/aggregate.rs
@@ -74,13 +74,16 @@ impl PlainAggregateWindowExpr {
         eq_properties: &mut EquivalenceProperties,
         window_expr_index: usize,
     ) {
-        let Some(expr) = self
+        if let Some(expr) = self
             .get_aggregate_expr()
-            .natural_sort_expr(window_expr_index)
-        else {
-            return;
-        };
-        add_new_ordering_expr_with_partition_by(eq_properties, expr, &self.partition_by);
+            .get_result_ordering(window_expr_index)
+        {
+            add_new_ordering_expr_with_partition_by(
+                eq_properties,
+                expr,
+                &self.partition_by,
+            );
+        }
     }
 }
 
diff --git a/datafusion/physical-expr/src/window/sliding_aggregate.rs b/datafusion/physical-expr/src/window/sliding_aggregate.rs
index 4752b264d752..23967e78f07a 100644
--- a/datafusion/physical-expr/src/window/sliding_aggregate.rs
+++ b/datafusion/physical-expr/src/window/sliding_aggregate.rs
@@ -22,14 +22,11 @@ use std::ops::Range;
 use std::sync::Arc;
 
 use crate::aggregate::AggregateFunctionExpr;
-use crate::window::standard::add_new_ordering_expr_with_partition_by;
 use crate::window::window_expr::AggregateWindowExpr;
 use crate::window::{
     PartitionBatches, PartitionWindowAggStates, PlainAggregateWindowExpr, WindowExpr,
 };
-use crate::{
-    expressions::PhysicalSortExpr, reverse_order_bys, EquivalenceProperties, PhysicalExpr,
-};
+use crate::{expressions::PhysicalSortExpr, reverse_order_bys, PhysicalExpr};
 
 use arrow::array::{Array, ArrayRef};
 use arrow::datatypes::Field;
@@ -70,20 +67,6 @@ impl SlidingAggregateWindowExpr {
     pub fn get_aggregate_expr(&self) -> &AggregateFunctionExpr {
         &self.aggregate
     }
-
-    pub fn add_equal_orderings(
-        &self,
-        eq_properties: &mut EquivalenceProperties,
-        window_expr_index: usize,
-    ) {
-        let Some(expr) = self
-            .get_aggregate_expr()
-            .natural_sort_expr(window_expr_index)
-        else {
-            return;
-        };
-        add_new_ordering_expr_with_partition_by(eq_properties, expr, &self.partition_by);
-    }
 }
 
 /// Incrementally update window function using the fact that batch is
diff --git a/datafusion/physical-expr/src/window/standard.rs b/datafusion/physical-expr/src/window/standard.rs
index 81038ae86e48..0c0bdf7e99cd 100644
--- a/datafusion/physical-expr/src/window/standard.rs
+++ b/datafusion/physical-expr/src/window/standard.rs
@@ -65,8 +65,7 @@ impl StandardWindowExpr {
         &self.expr
     }
 
-    /// Adds any equivalent orderings generated by the `self.expr`
-    /// to `builder`.
+    /// Adds any equivalent orderings generated by the `self.expr` to `builder`.
     ///
     /// If `self.expr` doesn't have an ordering, ordering equivalence properties
     /// are not updated. Otherwise, ordering equivalence properties are updated
diff --git a/datafusion/physical-plan/src/aggregates/mod.rs b/datafusion/physical-plan/src/aggregates/mod.rs
index 11463b1c27d3..fc129fe241e5 100644
--- a/datafusion/physical-plan/src/aggregates/mod.rs
+++ b/datafusion/physical-plan/src/aggregates/mod.rs
@@ -667,7 +667,7 @@ impl AggregateExec {
         // if the aggregate function is set monotonic, add it into equivalence properties
         for (i, aggr_expr) in aggr_exprs.iter().enumerate() {
             let aggr_expr_index = aggr_expr_indices[i];
-            if let Some(expr) = aggr_expr.natural_sort_expr(aggr_expr_index) {
+            if let Some(expr) = aggr_expr.get_result_ordering(aggr_expr_index) {
                 if group_expr_mapping.map.is_empty() {
                     eq_properties.add_new_ordering(LexOrdering::new(vec![expr]));
                 } else if *input_order_mode != InputOrderMode::Linear {
diff --git a/datafusion/physical-plan/src/windows/mod.rs b/datafusion/physical-plan/src/windows/mod.rs
index dcd2953acdab..24715c497fc3 100644
--- a/datafusion/physical-plan/src/windows/mod.rs
+++ b/datafusion/physical-plan/src/windows/mod.rs
@@ -354,11 +354,13 @@ pub(crate) fn window_equivalence_properties(
         {
             aggregate_udf_window_expr
                 .add_equal_orderings(&mut window_eq_properties, window_expr_index);
-        } else if let Some(aggregate_udf_window_expr) =
-            expr.as_any().downcast_ref::<SlidingAggregateWindowExpr>()
+        } else if let Some(_) = expr.as_any().downcast_ref::<SlidingAggregateWindowExpr>()
         {
-            aggregate_udf_window_expr
-                .add_equal_orderings(&mut window_eq_properties, window_expr_index);
+            // TODO: SlidingAggregateWindowExpr cannot introduce a new ordering yet
+            //       because we cannot determine whether the window's incoming elements
+            //       are greater than its outgoing elements. However, we do have
+            //       the necessary tools to support this, and we can extend support
+            //       for these cases in the future.
         }
     }
     window_eq_properties