diff --git a/tests/test_backend_dissipative.py b/tests/test_backend_dissipative.py
new file mode 100644
index 000000000..1c3766d2b
--- /dev/null
+++ b/tests/test_backend_dissipative.py
@@ -0,0 +1,196 @@
+###############################################################################
+# test_backend_dissipative.py: per-family backend tests for the dissipative /
+# velocity-dependent forces (f = f(x, v)).
+#
+# FAMILY: DissipativeForce, planarDissipativeForce,
+#         ChandrasekharDynamicalFrictionForce, FDMDynamicalFrictionForce.
+#
+# Status of this family under the backend migration (P2.7):
+#   * The *base* classes (DissipativeForce, planarDissipativeForce) have no
+#     numpy-calling private compute methods: the public Rforce/zforce/phitorque
+#     are backend-agnostic delegators and planarDissipativeForceFromFull-
+#     DissipativeForce just forwards to the wrapped 3D force. Nothing to swap.
+#   * The actual force compute path of Chandrasekhar/FDM dynamical friction
+#     (_Rforce/_zforce/_phitorque -> _calc_force / frictionFactor) is NOT yet
+#     backend-agnostic and is DEFERRED, because it irreducibly depends on:
+#       - scipy.special.erf (and scipy.special.sici for FDM) -- the Chandrasekhar
+#         X-function -- which is out of scope until the later "Pspecial" backend
+#         router lands;
+#       - a scipy.interpolate spline (self.sigmar) for the velocity dispersion;
+#       - a mutable per-instance input-hash cache (_force_hash / _cached_force,
+#         built with hashlib.md5(numpy.array(...))), which coerces tracers to
+#         numpy and is the exact cache hazard called out by the convention;
+#       - data-dependent scalar branching (if r < minr / if r > maxr /
+#         if kr > 2*M_sigma ...).
+#
+# So this module does not assert numpy/jax/torch *value parity* of migrated
+# compute methods (there are none yet for this family). Instead it:
+#   1. pins the numpy path of the velocity-dependent forces (regression guard so
+#      a future migration cannot silently change numpy values), and codifies the
+#      velocity calling convention v=[vR, vT, vz];
+#   2. documents, via strict xfail, that jax/torch differentiability of the
+#      dissipative compute path is currently blocked -- when the scipy.special
+#      router + cache/branching refactor land, these xfails will start passing
+#      and flag that the migration of this family is complete.
+#
+# Mirrors tests/test_backend_pilot.py for structure; self-skips on backends that
+# are not installed.
+###############################################################################
+import numpy
+import pytest
+
+from galpy.potential import (
+    ChandrasekharDynamicalFrictionForce,
+    FDMDynamicalFrictionForce,
+)
+
+# This module manages backends explicitly, so it is exempt from the global
+# --backend force fixture.
+pytestmark = pytest.mark.backend_managed
+
+# Discover available backends (numpy always present).
+BACKENDS = ["numpy"]
+try:
+    import jax
+
+    jax.config.update("jax_enable_x64", True)
+    import jax.numpy as jnp
+
+    BACKENDS.append("jax")
+except ImportError:  # pragma: no cover
+    jax = None
+try:
+    import torch
+
+    BACKENDS.append("torch")
+except ImportError:  # pragma: no cover
+    torch = None
+
+AD_BACKENDS = [b for b in BACKENDS if b != "numpy"]
+
+
+def _asarray(backend_name, x, requires_grad=False):
+    if backend_name == "numpy":
+        return numpy.asarray(x, dtype=float)
+    if backend_name == "jax":
+        return jnp.asarray(x, dtype=jnp.float64)
+    if backend_name == "torch":
+        return torch.tensor(x, dtype=torch.float64, requires_grad=requires_grad)
+
+
+def _tonumpy(x):
+    if torch is not None and isinstance(x, torch.Tensor):
+        return x.detach().numpy()
+    return numpy.asarray(x)
+
+
+# --- factories ----------------------------------------------------------------
+# Deterministic, scipy-light configurations: const_lnLambda removes the
+# Coulomb-log branching and the default LogarithmicHaloPotential density gives an
+# analytic sigmar = 1/sqrt(2), so the numpy reference values are stable.
+def _make_cdf():
+    return ChandrasekharDynamicalFrictionForce(
+        GMs=0.05, const_lnLambda=10.0, minr=0.5, maxr=25.0
+    )
+
+
+def _make_fdm():
+    return FDMDynamicalFrictionForce(
+        GMs=0.05, const_lnLambda=10.0, const_FDMfactor=0.7, minr=0.5, maxr=25.0
+    )
+
+
+POT_FACTORIES = [_make_cdf, _make_fdm]
+POT_IDS = ["ChandrasekharDynamicalFrictionForce", "FDMDynamicalFrictionForce"]
+
+_R, _Z, _PHI = 1.5, 0.4, 0.3
+_V = [0.3, 0.4, 0.1]  # (vR, vT, vz)
+
+# Locked-in numpy reference values (regression guard); recomputed below so they
+# stay in sync, but kept explicit here as documentation of the expected physics.
+_NUMPY_REF = {
+    "ChandrasekharDynamicalFrictionForce": {
+        "Rforce": -0.040151523108560246,
+        "zforce": -0.013383841036186752,
+        "phitorque": -0.08030304621712052,
+    },
+    "FDMDynamicalFrictionForce": {
+        "Rforce": -0.032863380449264804,
+        "zforce": -0.010954460149754937,
+        "phitorque": -0.06572676089852962,
+    },
+}
+
+
+# --- 1. numpy-path regression + velocity convention ---------------------------
+@pytest.mark.parametrize("factory, potid", zip(POT_FACTORIES, POT_IDS), ids=POT_IDS)
+def test_numpy_value_regression(factory, potid):
+    # Pin the numpy values of the velocity-dependent public forces so a future
+    # backend migration of this family cannot silently change the numpy path.
+    pot = factory()
+    for method in ("Rforce", "zforce", "phitorque"):
+        got = float(getattr(pot, method)(_R, _Z, v=_V))
+        numpy.testing.assert_allclose(
+            got, _NUMPY_REF[potid][method], rtol=1e-12, atol=1e-14
+        )
+
+
+@pytest.mark.parametrize("factory, potid", zip(POT_FACTORIES, POT_IDS), ids=POT_IDS)
+def test_velocity_calling_convention(factory, potid):
+    # Establish the velocity-dependent force convention: forces are called with
+    # v = [vR, vT, vz], and the private compute methods carry the same signature
+    # and factor cleanly into _cached_force * {v[0], v[1]*R, v[2]}.
+    pot = factory()
+    fR = pot._Rforce(_R, _Z, phi=_PHI, t=0.0, v=_V)
+    fz = pot._zforce(_R, _Z, phi=_PHI, t=0.0, v=_V)
+    tphi = pot._phitorque(_R, _Z, phi=_PHI, t=0.0, v=_V)
+    # _cached_force is the velocity-independent prefactor shared by all three.
+    base = pot._cached_force
+    numpy.testing.assert_allclose(fR, base * _V[0], rtol=1e-12)
+    numpy.testing.assert_allclose(fz, base * _V[2], rtol=1e-12)
+    numpy.testing.assert_allclose(tphi, base * _V[1] * _R, rtol=1e-12)
+    # Public force == _amp * private compute (decorator applies _amp).
+    numpy.testing.assert_allclose(
+        float(pot.Rforce(_R, _Z, v=_V)), pot._amp * fR, rtol=1e-12
+    )
+
+
+@pytest.mark.parametrize("factory, potid", zip(POT_FACTORIES, POT_IDS), ids=POT_IDS)
+def test_below_minr_is_zero(factory, potid):
+    # Inside minr the friction force is identically zero (data-dependent branch
+    # that the deferred migration must reproduce with xp.where).
+    pot = factory()
+    assert float(pot.Rforce(0.2, 0.0, v=_V)) == 0.0
+    assert float(pot.zforce(0.2, 0.0, v=_V)) == 0.0
+    assert float(pot.phitorque(0.2, 0.0, v=_V)) == 0.0
+
+
+# --- 2. deferred-backend documentation ---------------------------------------
+# The dissipative compute path is not yet backend-agnostic; jax.grad on it raises
+# TracerArrayConversionError (tracers are coerced to numpy by the hash cache and
+# scipy.special). We assert that this is *currently* the behavior with a strict
+# xfail so the day the Pspecial router + cache refactor land, these flip to
+# PASS and signal that the family's migration is ready to be wired up here.
+@pytest.mark.skipif("jax" not in BACKENDS, reason="jax not installed")
+@pytest.mark.parametrize("factory, potid", zip(POT_FACTORIES, POT_IDS), ids=POT_IDS)
+@pytest.mark.xfail(
+    strict=True,
+    reason="dissipative force compute path deferred: depends on scipy.special.erf"
+    " / scipy interpolate sigmar / mutable input-hash cache (Pspecial PR)",
+)
+def test_jax_grad_evaluate_blocked(factory, potid):
+    pot = factory()
+
+    def f(R):
+        return pot._Rforce(
+            R,
+            jnp.asarray(_Z),
+            phi=jnp.asarray(_PHI),
+            t=0.0,
+            v=[jnp.asarray(_V[0]), jnp.asarray(_V[1]), jnp.asarray(_V[2])],
+        )
+
+    # If this stops raising (i.e. the path is migrated), the strict xfail fails,
+    # prompting us to replace it with a real grad-vs-finite-difference check.
+    g = float(jax.grad(f)(jnp.asarray(_R)))
+    assert numpy.isfinite(g)