Non-Arrhenius Transport Behaviors

• Non-Arrhenius transport behavior is defined by deviations from the classical Arrhenius law due to heterogeneous activation barriers and correlated events.
• Experimental results reveal that disorder, microstructure, and entropic contributions manifest as upward or downward curvature in Arrhenius plots.
• Generalized models, including fractional calculus and non-additive stochastic approaches, accurately capture nonlinear temperature and field-dependent transport phenomena.

Non-Arrhenius transport behavior encompasses a broad class of phenomena in which measurable transport coefficients—such as ionic conductivity, diffusivity, mobility, or viscosity—exhibit temperature or field dependence that deviates from the classical Arrhenius law $X(T) = X_0 \exp(-E_a/(k_BT))$, where $E_a$ is the activation energy. This nonlinear response is observed in numerous settings, including disordered materials, crystalline polymorphs, glasses, supercooled liquids, and engineered interfaces. Mechanistically, non-Arrhenius behavior can result from spatial or temporal heterogeneity in activation barriers, many-body correlations, system-size effects, entropic contributions, and nonequilibrium dynamics.

1. Fundamental Origins of Non-Arrhenius Behavior

Non-Arrhenius transport is most fundamentally tied to two effects: distributions of activation energies and correlated (non-Poissonian) transport events. In ideal crystals, each mobile species encounters a uniform energy barrier, leading to a simple exponential (Arrhenius) dependence. However, in glasses and disordered systems, the potential energy landscape is spatially heterogeneous, leading to a distribution of local activation energies $g(\Delta E)$ (Bischoff et al., 2012). Transport must then be described by a temperature-dependent expectation $\langle \Delta E \rangle$,

$$\langle \Delta E \rangle = \int_0^\infty \Delta E \cdot P(\Delta E, T) \, d\Delta E,$$

where $P(\Delta E, T)$ is a Boltzmann-weighted probability. For a Gaussian distribution, $$\langle \Delta E \rangle \approx \Delta E_0 - \delta^2/(RT)$$, resulting in quadratic curvature in Arrhenius plots.

Additionally, time-correlated or many-body hopping processes, such as concerted closed-loop motion in crystalline polymorphs (Morgan et al., 2014), break the assumption of independent Poisson jumps and destroy the direct correspondence between single-ion activation energies and ensemble transport.

2. Disorder, Microstructure, and Activation Energy Distributions

Structural, compositional, and interface disorder fundamentally alter the transport landscape. In glasses, cation site disorder broadens the distribution of activation energies, amplifying non-Arrhenius effects (Bischoff et al., 2012). In amorphous oxide thin-film transistors, interface trap-induced disorder introduces spatial fluctuations of the conduction mobility edge $E_c$, well-modeled by a Gaussian distribution. The effective activation energy,

$$E_{aeff}(T, N_{ST}) = \alpha - \frac{q\beta^2}{2kT}$$

where $\alpha$ and $\beta$ scale with the trap density $N_{ST}$, decreases as temperature lowers and disorder increases, leading to upward curvature on Arrhenius plots and variable-range hopping at low temperatures (Benwadih et al., 2015).

Microstructure effects have been clearly demonstrated in argyrodite solid electrolytes (Ou et al., 20 Oct 2025): at high temperature, bulk conduction dominates and follows an Arrhenius law with higher $E_a$. Below a crossover temperature (e.g., $\sim$250 K in Li$_6$PS$_5$I), faster grain boundary channels with lower activation barriers take over, producing non-Arrhenius behavior.

3. Entropic Contributions and Free Energy Barriers

Beyond the energetic landscape, entropic effects are crucial in certain regimes. In minimal glassy systems, the measured free energy barrier $F_b$ governing structural rearrangements can be decomposed as $F_b = U_b - TS_b$ (in units of energy), where $U_b$ is the energetic component and $S_b$ the entropic one (Du et al., 2015). As temperature drops or the system becomes crowded, the scarcity of transition pathways increases $S_b$, causing super-Arrhenius scaling of transition times $\tau \propto \exp(\beta F_b)$, observed near the glass transition.

In dislocation mechanics, at stresses near the critical resolved shear stress, the potential energy barrier may vanish, and the activation entropy term $T\Delta S$ controls the rate, inducing transitions between anti-Arrhenius and classical Arrhenius kinetics as temperature increases (Nahavandian et al., 8 Jan 2024).

4. Many-body Effects and Temporal Correlations

Time-correlated or many-body transport events defy the assumptions of single-particle activated hopping. Crystal polymorphs of AgI exhibit markedly different behaviors depending on structural coordination: rocksalt AgI (B1) supports open chain hopping reminiscent of independent defect motion and is well-described by modified Arrhenius laws, whereas zincblende/wurtzite phases (B3, B4) have concerted closed-loop chains that strongly suppress net charge transport, producing non-Arrhenius conductivity and a breakdown of the Nernst–Einstein relation (Morgan et al., 2014). Such many-body effects can be captured through analysis of diffusion chains and chain-length dependent free energies.

Similarly, simulations of small polaron transport show that transient lattice relaxation (delayed polaron formation) or the presence of immovable boundaries can induce anomalous transport scaling (non-diffusive, subdiffusive, or superdiffusive MSD behavior), breaking Arrhenius expectations (Bhattacharyya et al., 2023). The topology and local environment (open vs. periodic chains) significantly affect mobility computations.

5. Nonequilibrium and Stochastic Model Approaches

Several theoretical frameworks generalize the classical Arrhenius law to capture non-linear and non-exponential transport behavior. Fractional calculus modifies the Van’t Hoff equation by introducing derivatives of fractional order $\alpha$, leading to solutions like

$$k(T) = A \exp \left( \frac{\Gamma(2 - \alpha)\cos(\pi\alpha) E}{R T^{2-\alpha}} \right)$$

which better fit experimental data displaying curvature in Arrhenius plots (Lemes et al., 2016).

Non-additive stochastic models, motivated by generalized Fokker–Planck or continuity equations, provide flexible descriptions of diffusive and viscous transport in supercooled liquids and glasses (Junior et al., 2019, Junior et al., 30 Mar 2024). In these models, the temperature-dependent diffusivity is expressed as

$D(T) = D_0 [1 - (2-m) E/(k_BT)]^{1/(2-m)},$

recovering Arrhenius law for $m \rightarrow 2$, with super-Arrhenius ($m < 2$) and sub-Arrhenius ($m > 2$) regimes distinguished by fragility indices and activation energies that diverge or flatten with temperature.

Theoretical treatments of transport in complex fluids adopt environment-coupled diffusion kernels and time correlation functions, capturing contributions from intrinsic (non-Poissonian) and extrinsic (environmental) disorder. Non-Gaussian statistics and time-dependent relaxation of displacement distributions further lead to non-exponential temperature dependencies (Song et al., 2018).

6. Experimental Signatures and Implications

Non-Arrhenius behavior manifests through characteristic “upward” or “downward” curvature in Arrhenius plots (log of transport coefficient vs. inverse temperature), crossovers between distinct transport regimes (bulk-dominated vs. boundary-dominated), and divergence or atypical scaling of activation energies and viscosities near critical temperatures.

Experimentally, glassy sodium sulphide–germanium sulphide–phosphate mixtures (Bischoff et al., 2012) display clear curvature indicative of distributed activation energies, whereas amorphous InXZnO TFTs (Benwadih et al., 2015) transition from Arrhenius to percolative variable-range conductivity at low T. Argyrodite solid electrolytes (Ou et al., 20 Oct 2025) reveal grain-size-dependent non-Arrhenius transport, with design implications for superionic battery materials. Anharmonic effects in FCC metals elevate vacancy concentrations and alter diffusion rates (Cuong et al., 2022).

In supercooled liquids, the Non-additive Stochastic Model provides robust fits to viscosity data across numerous fragile and strong glass-formers and quantifies fragility via model parameters linking to Angell’s plot (Junior et al., 30 Mar 2024).

7. Broader Context: Nonequilibrium and Active Transport

Non-equilibrium Langevin approaches unveil exotic transport phenomena—giant amplification of velocity under nonthermal noise, multiple current reversals, and negative mobility—none of which are described by a static Arrhenius landscape (Spiechowicz et al., 3 Jun 2024, Wang et al., 2022). These effects arise due to synchronization between noise characteristics and intrinsic system timescales, non-local correlations, and periodic or stochastic driving.

In Markovian master equations, departures from Arrhenius rates (e.g., Fokker–Planck or destination rates) do not necessarily produce net transport currents in symmetric time-periodic fields, due to cancellation effects established by the no-pumping theorem (Martirosyan, 2017). This emphasizes the role of symmetry and rate structure in controlling non-Arrhenius transport.

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Overall, non-Arrhenius transport encompasses a spectrum of physical processes governed by disorder, correlations, entropic effects, and nonequilibrium dynamics. Quantitative models—spanning distributions of activation energies, generalized continuity equations, fractional calculus, and many-body simulation—provide critical tools for interpreting experimental observations and guiding materials design in glasses, electrolytes, semiconductors, polymer electronics, and beyond.