feos-org · prehner · Aug 20, 2026 · Aug 11, 2026
diff --git a/Cargo.toml b/Cargo.toml
@@ -22,8 +22,8 @@ keywords = [
 categories = ["science"]
 
 [workspace.dependencies]
-quantity = "0.14"
-num-dual = "0.14"
+quantity = "0.15"
+num-dual = "0.15"
 ndarray = "0.17"
 nalgebra = "0.35"
 thiserror = "2.0"

diff --git a/crates/feos-core/src/ad/mod.rs b/crates/feos-core/src/ad/mod.rs
@@ -10,7 +10,7 @@ mod properties;
 pub use dataset::*;
 pub use properties::*;
 
-pub(crate) type Gradient<const P: usize> = DualSVec<f64, f64, P>;
+pub(crate) type Gradient<const P: usize> = DualSVec<f64, P>;
 
 /// A model that can be evaluated with derivatives of its parameters.
 pub trait ParametersAD<N: Dim>: Residual<N>
@@ -23,7 +23,7 @@ where
     /// defines the canonical parameter order.
     ///
     /// Set `differentiable` to `false` for fixed parameters.
-    fn build<D: DualNum<f64, Inner = f64> + Copy>(
+    fn build<D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         f: impl FnMut(&'static str, bool) -> D,
     ) -> Self::Lifted<D>;
 
@@ -66,8 +66,7 @@ where
             idx += 1;
             let mut d = Gradient::<P>::from(parameter_values[i]);
             if let Some(seed_idx) = derivative_names.iter().position(|&n| n == name) {
-                d.eps =
-                    Derivative::<_, _, Const<P>, _>::derivative_generic(Const::<P>, U1, seed_idx);
+                d.eps = Derivative::<_, Const<P>, _>::derivative_generic(Const::<P>, U1, seed_idx);
             }
             d
         })

diff --git a/crates/feos-core/src/ad/properties/boiling_temperature.rs b/crates/feos-core/src/ad/properties/boiling_temperature.rs
@@ -22,7 +22,7 @@ where
     type Unit = _Temperature;
     const REFERENCE: Temperature = KELVIN;
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<Temperature<D>> {

diff --git a/crates/feos-core/src/ad/properties/bubble_point_pressure.rs b/crates/feos-core/src/ad/properties/bubble_point_pressure.rs
@@ -28,7 +28,7 @@ where
     type Unit = _Pressure;
     const REFERENCE: Pressure = PASCAL;
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<Pressure<D>>

diff --git a/crates/feos-core/src/ad/properties/dew_point_pressure.rs b/crates/feos-core/src/ad/properties/dew_point_pressure.rs
@@ -27,7 +27,7 @@ where
     type Unit = _Pressure;
     const REFERENCE: Pressure = PASCAL;
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<Pressure<D>>

diff --git a/crates/feos-core/src/ad/properties/enthalpy_of_vaporization.rs b/crates/feos-core/src/ad/properties/enthalpy_of_vaporization.rs
@@ -21,7 +21,7 @@ where
     type Unit = _MolarEnergy;
     const REFERENCE: MolarEnergy = MolarEnergy::new(1.0);
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<MolarEnergy<D>> {

diff --git a/crates/feos-core/src/ad/properties/equilibrium_liquid_density.rs b/crates/feos-core/src/ad/properties/equilibrium_liquid_density.rs
@@ -21,7 +21,7 @@ where
     type Unit = _Density;
     const REFERENCE: Density = Density::new(1000.0);
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<Density<D>> {

diff --git a/crates/feos-core/src/ad/properties/liquid_density.rs b/crates/feos-core/src/ad/properties/liquid_density.rs
@@ -23,7 +23,7 @@ where
     type Unit = _Density;
     const REFERENCE: Density = Density::new(1000.0);
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<Density<D>> {

diff --git a/crates/feos-core/src/ad/properties/mod.rs b/crates/feos-core/src/ad/properties/mod.rs
@@ -34,7 +34,7 @@ where
     const REFERENCE: Quantity<f64, Self::Unit>;
 
     /// Evaluate the property for an arbitrary derivative.
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<Quantity<D, Self::Unit>>;

diff --git a/crates/feos-core/src/ad/properties/residual_isobaric_heat_capacity.rs b/crates/feos-core/src/ad/properties/residual_isobaric_heat_capacity.rs
@@ -23,7 +23,7 @@ where
     type Unit = _MolarEntropy;
     const REFERENCE: MolarEntropy = MolarEntropy::new(1.0);
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<MolarEntropy<D>> {

diff --git a/crates/feos-core/src/ad/properties/vapor_pressure.rs b/crates/feos-core/src/ad/properties/vapor_pressure.rs
@@ -22,7 +22,7 @@ where
     type Unit = _Pressure;
     const REFERENCE: Pressure = PASCAL;
 
-    fn evaluate<E: Residual<N, D>, D: DualNum<f64, Inner = f64> + Copy>(
+    fn evaluate<E: Residual<N, D>, D: DualNum<Primitive = f64, Inner = f64> + Copy>(
         &self,
         eos: &E,
     ) -> FeosResult<Pressure<D>> {

diff --git a/crates/feos-core/src/cubic.rs b/crates/feos-core/src/cubic.rs
@@ -121,11 +121,11 @@ impl ResidualDyn for PengRobinson {
         self.tc.len()
     }
 
-    fn compute_max_density<D: DualNum<f64> + Copy>(&self, molefracs: &DVector<D>) -> D {
+    fn compute_max_density<D: DualNum<Primitive = f64> + Copy>(&self, molefracs: &DVector<D>) -> D {
         D::from(0.9) / molefracs.dot(&self.b.map(D::from))
     }
 
-    fn reduced_helmholtz_energy_density_contributions<D: DualNum<f64> + Copy>(
+    fn reduced_helmholtz_energy_density_contributions<D: DualNum<Primitive = f64> + Copy>(
         &self,
         state: &StateHD<D>,
     ) -> Vec<(&'static str, D)> {

diff --git a/crates/feos-core/src/density_iteration.rs b/crates/feos-core/src/density_iteration.rs
@@ -6,7 +6,7 @@ use nalgebra::{DefaultAllocator, Dim, OVector};
 use num_dual::{Dual, DualNum, first_derivative};
 use quantity::{Density, Pressure, Temperature};
 
-pub fn density_iteration<E: Residual<N, D>, N: Dim, D: DualNum<f64> + Copy>(
+pub fn density_iteration<E: Residual<N, D>, N: Dim, D: DualNum<Primitive = f64> + Copy>(
     eos: &E,
     temperature: Temperature<D>,
     pressure: Pressure<D>,

diff --git a/crates/feos-core/src/equation_of_state/mod.rs b/crates/feos-core/src/equation_of_state/mod.rs
@@ -53,11 +53,11 @@ impl<I, R: ResidualDyn> ResidualDyn for EquationOfState<Vec<I>, R> {
         self.residual.components()
     }
 
-    fn compute_max_density<D: DualNum<f64> + Copy>(&self, molefracs: &DVector<D>) -> D {
+    fn compute_max_density<D: DualNum<Primitive = f64> + Copy>(&self, molefracs: &DVector<D>) -> D {
         self.residual.compute_max_density(molefracs)
     }
 
-    fn reduced_helmholtz_energy_density_contributions<D: DualNum<f64> + Copy>(
+    fn reduced_helmholtz_energy_density_contributions<D: DualNum<Primitive = f64> + Copy>(
         &self,
         state: &StateHD<D>,
     ) -> Vec<(&'static str, D)> {
@@ -79,19 +79,20 @@ impl<I: Clone, R: Subset> Subset for EquationOfState<Vec<I>, R> {
     }
 }
 
-impl<I: Clone, R: Residual<Const<N>, D>, D: DualNum<f64> + Copy, const N: usize>
+impl<I: Clone, R: Residual<Const<N>, D>, D: DualNum<Primitive = f64> + Copy, const N: usize>
     Residual<Const<N>, D> for EquationOfState<[I; N], R>
 {
     fn components(&self) -> usize {
         N
     }
 
     type Real = EquationOfState<[I; N], R::Real>;
-    type Lifted<D2: DualNum<f64, Inner = D> + Copy> = EquationOfState<[I; N], R::Lifted<D2>>;
+    type Lifted<D2: DualNum<Primitive = f64, Inner = D> + Copy> =
+        EquationOfState<[I; N], R::Lifted<D2>>;
     fn re(&self) -> Self::Real {
         EquationOfState::new(self.ideal_gas.clone(), self.residual.re())
     }
-    fn lift<D2: DualNum<f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2> {
+    fn lift<D2: DualNum<Primitive = f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2> {
         EquationOfState::new(self.ideal_gas.clone(), self.residual.lift())
     }
 
@@ -118,7 +119,7 @@ pub trait IdealGas {
     /// Implementation of an ideal gas model in terms of the
     /// logarithm of the cubic thermal de Broglie wavelength
     /// in units ln(A³) for each component in the system.
-    fn ln_lambda3<D: DualNum<f64> + Copy>(&self, temperature: D) -> D;
+    fn ln_lambda3<D: DualNum<Primitive = f64> + Copy>(&self, temperature: D) -> D;
 
     /// The name of the ideal gas model.
     fn ideal_gas_model(&self) -> &'static str;
@@ -128,9 +129,9 @@ pub trait IdealGas {
 /// respect to parameters.
 pub trait IdealGasAD<D = f64>: Clone {
     type Real: IdealGasAD;
-    type Lifted<D2: DualNum<f64, Inner = D> + Copy>: IdealGasAD<D2>;
+    type Lifted<D2: DualNum<Primitive = f64, Inner = D> + Copy>: IdealGasAD<D2>;
     fn re(&self) -> Self::Real;
-    fn lift<D2: DualNum<f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2>;
+    fn lift<D2: DualNum<Primitive = f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2>;
 
     /// Implementation of an ideal gas model in terms of the
     /// logarithm of the cubic thermal de Broglie wavelength
@@ -142,14 +143,14 @@ pub trait IdealGasAD<D = f64>: Clone {
 }
 
 /// A total Helmholtz energy model consisting of a [Residual] model and an [IdealGas] part.
-pub trait Total<N: Dim = Dyn, D: DualNum<f64> + Copy = f64>: Residual<N, D>
+pub trait Total<N: Dim = Dyn, D: DualNum<Primitive = f64> + Copy = f64>: Residual<N, D>
 where
     DefaultAllocator: Allocator<N>,
 {
     type RealTotal: Total<N, f64>;
-    type LiftedTotal<D2: DualNum<f64, Inner = D> + Copy>: Total<N, D2>;
+    type LiftedTotal<D2: DualNum<Primitive = f64, Inner = D> + Copy>: Total<N, D2>;
     fn re_total(&self) -> Self::RealTotal;
-    fn lift_total<D2: DualNum<f64, Inner = D> + Copy>(&self) -> Self::LiftedTotal<D2>;
+    fn lift_total<D2: DualNum<Primitive = f64, Inner = D> + Copy>(&self) -> Self::LiftedTotal<D2>;
 
     fn ideal_gas_model(&self) -> &'static str;
 
@@ -199,15 +200,15 @@ impl<
     I: IdealGas + 'static,
     C: Deref<Target = EquationOfState<Vec<I>, R>> + Clone,
     R: ResidualDyn + 'static,
-    D: DualNum<f64> + Copy,
+    D: DualNum<Primitive = f64> + Copy,
 > Total<Dyn, D> for C
 {
     type RealTotal = Self;
-    type LiftedTotal<D2: DualNum<f64, Inner = D> + Copy> = Self;
+    type LiftedTotal<D2: DualNum<Primitive = f64, Inner = D> + Copy> = Self;
     fn re_total(&self) -> Self::RealTotal {
         self.clone()
     }
-    fn lift_total<D2: DualNum<f64, Inner = D> + Copy>(&self) -> Self::LiftedTotal<D2> {
+    fn lift_total<D2: DualNum<Primitive = f64, Inner = D> + Copy>(&self) -> Self::LiftedTotal<D2> {
         self.clone()
     }
 
@@ -225,19 +226,19 @@ impl<
     }
 }
 
-impl<I: IdealGasAD<D>, R: Residual<Const<N>, D>, D: DualNum<f64> + Copy, const N: usize>
+impl<I: IdealGasAD<D>, R: Residual<Const<N>, D>, D: DualNum<Primitive = f64> + Copy, const N: usize>
     Total<Const<N>, D> for EquationOfState<[I; N], R>
 {
     type RealTotal = EquationOfState<[I::Real; N], R::Real>;
-    type LiftedTotal<D2: DualNum<f64, Inner = D> + Copy> =
+    type LiftedTotal<D2: DualNum<Primitive = f64, Inner = D> + Copy> =
         EquationOfState<[I::Lifted<D2>; N], R::Lifted<D2>>;
     fn re_total(&self) -> Self::RealTotal {
         EquationOfState::new(
             self.ideal_gas.each_ref().map(|i| i.re()),
             self.residual.re(),
         )
     }
-    fn lift_total<D2: DualNum<f64, Inner = D> + Copy>(&self) -> Self::LiftedTotal<D2> {
+    fn lift_total<D2: DualNum<Primitive = f64, Inner = D> + Copy>(&self) -> Self::LiftedTotal<D2> {
         EquationOfState::new(
             self.ideal_gas.each_ref().map(|i| i.lift()),
             self.residual.lift(),

diff --git a/crates/feos-core/src/equation_of_state/residual.rs b/crates/feos-core/src/equation_of_state/residual.rs
@@ -15,15 +15,15 @@ type Quot<T1, T2> = <T1 as Div<T2>>::Output;
 /// Molar weight of all components.
 ///
 /// Enables calculation of (mass) specific properties.
-pub trait Molarweight<N: Dim = Dyn, D: DualNum<f64> + Copy = f64>
+pub trait Molarweight<N: Dim = Dyn, D: DualNum<Primitive = f64> + Copy = f64>
 where
     DefaultAllocator: Allocator<N>,
 {
     fn molar_weight(&self) -> MolarWeight<OVector<D, N>>;
 }
 
-impl<C: Deref<Target = T>, T: Molarweight<N, D>, N: Dim, D: DualNum<f64> + Copy> Molarweight<N, D>
-    for C
+impl<C: Deref<Target = T>, T: Molarweight<N, D>, N: Dim, D: DualNum<Primitive = f64> + Copy>
+    Molarweight<N, D> for C
 where
     DefaultAllocator: Allocator<N>,
 {
@@ -62,23 +62,25 @@ pub trait ResidualDyn {
     /// equilibria and other iterations. It is not explicitly meant to
     /// be a mathematical limit for the density (if those exist in the
     /// equation of state anyways).
-    fn compute_max_density<D: DualNum<f64> + Copy>(&self, molefracs: &DVector<D>) -> D;
+    fn compute_max_density<D: DualNum<Primitive = f64> + Copy>(&self, molefracs: &DVector<D>) -> D;
 
     /// Evaluate the reduced Helmholtz energy density of each individual contribution
     /// and return them together with a string representation of the contribution.
-    fn reduced_helmholtz_energy_density_contributions<D: DualNum<f64> + Copy>(
+    fn reduced_helmholtz_energy_density_contributions<D: DualNum<Primitive = f64> + Copy>(
         &self,
         state: &StateHD<D>,
     ) -> Vec<(&'static str, D)>;
 }
 
-impl<C: Deref<Target = T> + Clone, T: ResidualDyn, D: DualNum<f64> + Copy> Residual<Dyn, D> for C {
+impl<C: Deref<Target = T> + Clone, T: ResidualDyn, D: DualNum<Primitive = f64> + Copy>
+    Residual<Dyn, D> for C
+{
     type Real = Self;
-    type Lifted<D2: DualNum<f64, Inner = D> + Copy> = Self;
+    type Lifted<D2: DualNum<Primitive = f64, Inner = D> + Copy> = Self;
     fn re(&self) -> Self::Real {
         self.clone()
     }
-    fn lift<D2: DualNum<f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2> {
+    fn lift<D2: DualNum<Primitive = f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2> {
         self.clone()
     }
     fn components(&self) -> usize {
@@ -96,7 +98,7 @@ impl<C: Deref<Target = T> + Clone, T: ResidualDyn, D: DualNum<f64> + Copy> Resid
 }
 
 /// A residual Helmholtz energy model.
-pub trait Residual<N: Dim = Dyn, D: DualNum<f64> + Copy = f64>: Clone
+pub trait Residual<N: Dim = Dyn, D: DualNum<Primitive = f64> + Copy = f64>: Clone
 where
     DefaultAllocator: Allocator<N>,
 {
@@ -114,13 +116,13 @@ where
     type Real: Residual<N>;
 
     /// The residual model with the model parameters lifted to a higher dual number.
-    type Lifted<D2: DualNum<f64, Inner = D> + Copy>: Residual<N, D2>;
+    type Lifted<D2: DualNum<Primitive = f64, Inner = D> + Copy>: Residual<N, D2>;
 
     /// Return the real part of the residual model.
     fn re(&self) -> Self::Real;
 
     /// Return the lifted residual model.
-    fn lift<D2: DualNum<f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2>;
+    fn lift<D2: DualNum<Primitive = f64, Inner = D> + Copy>(&self) -> Self::Lifted<D2>;
 
     /// Return the maximum density in Angstrom^-3.
     ///
@@ -303,7 +305,7 @@ where
         molefracs: &OVector<D, N>,
     ) -> (D, D, D, D, D) {
         let molar_volume = density.recip();
-        let (a, da, d2a) = hessian::<_, _, _, U2, _>(
+        let (a, da, d2a) = hessian::<_, _, U2, _>(
             partial(
                 |vt: SVector<_, 2>, x: &OVector<_, N>| {
                     let [[v, t]] = vt.data.0;
@@ -418,7 +420,7 @@ where
 }
 
 /// Reference values and residual entropy correlations for entropy scaling.
-pub trait EntropyScaling<N: Dim = Dyn, D: DualNum<f64> + Copy = f64>
+pub trait EntropyScaling<N: Dim = Dyn, D: DualNum<Primitive = f64> + Copy = f64>
 where
     DefaultAllocator: Allocator<N>,
 {
@@ -445,7 +447,7 @@ where
     fn thermal_conductivity_correlation(&self, s_res: D, x: &OVector<D, N>) -> D;
 }
 
-impl<C: Deref<Target = T>, T: EntropyScaling<N, D>, N: Dim, D: DualNum<f64> + Copy>
+impl<C: Deref<Target = T>, T: EntropyScaling<N, D>, N: Dim, D: DualNum<Primitive = f64> + Copy>
     EntropyScaling<N, D> for C
 where
     DefaultAllocator: Allocator<N>,
@@ -502,11 +504,11 @@ impl ResidualDyn for NoResidual {
         self.0
     }
 
-    fn compute_max_density<D: DualNum<f64> + Copy>(&self, _: &DVector<D>) -> D {
+    fn compute_max_density<D: DualNum<Primitive = f64> + Copy>(&self, _: &DVector<D>) -> D {
         D::one()
     }
 
-    fn reduced_helmholtz_energy_density_contributions<D: DualNum<f64> + Copy>(
+    fn reduced_helmholtz_energy_density_contributions<D: DualNum<Primitive = f64> + Copy>(
         &self,
         _: &StateHD<D>,
     ) -> Vec<(&'static str, D)> {

diff --git a/crates/feos-core/src/lib.rs b/crates/feos-core/src/lib.rs
@@ -221,7 +221,7 @@ mod tests {
             "NoIdealGas"
         }
 
-        fn ln_lambda3<D: DualNum<f64> + Copy>(&self, _: D) -> D {
+        fn ln_lambda3<D: DualNum<Primitive = f64> + Copy>(&self, _: D) -> D {
             unreachable!()
         }
     }