diff --git a/pytensor/graph/rewriting/db.py b/pytensor/graph/rewriting/db.py
index fb81622458..fc18636a1a 100644
--- a/pytensor/graph/rewriting/db.py
+++ b/pytensor/graph/rewriting/db.py
@@ -310,18 +310,21 @@ class EquilibriumDB(RewriteDatabase):
     """
 
     def __init__(
-        self, ignore_newtrees: bool = True, tracks_on_change_inputs: bool = False
+        self,
+        ignore_newtrees: bool = True,
+        tracks_on_change_inputs: bool = False,
+        eq_rewriter_class=pytensor_rewriting.EquilibriumGraphRewriter,
     ):
         """
 
         Parameters
         ----------
         ignore_newtrees
-            If ``False``, apply rewrites to new nodes introduced during
-            rewriting.
-
+            If ``False``, apply rewrites to new nodes introduced during rewritings.
         tracks_on_change_inputs
             If ``True``, re-apply rewrites on nodes with changed inputs.
+        eq_rewriter_class: EquilibriumGraphRewriter class, optional
+            The class used to create the equilibrium rewriter. Defaults to EquilibriumGraphRewriter.
 
         """
         super().__init__()
@@ -329,6 +332,7 @@ def __init__(
         self.tracks_on_change_inputs = tracks_on_change_inputs
         self.__final__: dict[str, bool] = {}
         self.__cleanup__: dict[str, bool] = {}
+        self.eq_rewriter_class = eq_rewriter_class
 
     def register(
         self,
@@ -360,7 +364,7 @@ def query(self, *tags, **kwtags):
             final_rewriters = None
         if len(cleanup_rewriters) == 0:
             cleanup_rewriters = None
-        return pytensor_rewriting.EquilibriumGraphRewriter(
+        return self.eq_rewriter_class(
             rewriters,
             max_use_ratio=config.optdb__max_use_ratio,
             ignore_newtrees=self.ignore_newtrees,
diff --git a/pytensor/scan/rewriting.py b/pytensor/scan/rewriting.py
index c5ac0a28a3..adab47d37b 100644
--- a/pytensor/scan/rewriting.py
+++ b/pytensor/scan/rewriting.py
@@ -30,6 +30,7 @@
 from pytensor.graph.op import compute_test_value
 from pytensor.graph.replace import clone_replace
 from pytensor.graph.rewriting.basic import (
+    EquilibriumGraphRewriter,
     GraphRewriter,
     copy_stack_trace,
     in2out,
@@ -2517,12 +2518,21 @@ def scan_push_out_dot1(fgraph, node):
     return False
 
 
+class ScanEquilibriumGraphRewriter(EquilibriumGraphRewriter):
+    """Subclass of EquilibriumGraphRewriter that aborts early if there are no Scan Ops in the graph"""
+
+    def apply(self, fgraph, start_from=None):
+        if not any(isinstance(node.op, Scan) for node in fgraph.apply_nodes):
+            return
+        super().apply(fgraph=fgraph, start_from=start_from)
+
+
 # I've added an equilibrium because later scan optimization in the sequence
 # can make it such that earlier optimizations should apply. However, in
 # general I do not expect the sequence to run more then once
-scan_eqopt1 = EquilibriumDB()
+scan_eqopt1 = EquilibriumDB(eq_rewriter_class=ScanEquilibriumGraphRewriter)
 scan_seqopt1 = SequenceDB()
-scan_eqopt2 = EquilibriumDB()
+scan_eqopt2 = EquilibriumDB(eq_rewriter_class=ScanEquilibriumGraphRewriter)
 
 # scan_eqopt1 before ShapeOpt at 0.1
 # This is needed to don't have ShapeFeature trac old Scan that we