NSI Thermal Potentials: Theory & Applications

• NSI thermal potentials are effective, temperature-dependent terms in governing equations that modify transport, energy exchange, and quantum dynamics across various systems.
• In superconducting devices and quantum transport, self-consistent circuit and quantum Boltzmann frameworks reveal that these potentials enhance cooling power, induce negative differential resistance, and enable thermal current control.
• They also affect neutrino oscillations and neuronal signal propagation, offering experimental pathways for optimizing devices and probing new physics.

Non-Standard Interaction (NSI) Thermal Potentials describe medium-induced modifications to transport, energy exchange, or quantum system dynamics associated with either particle propagation, device cooling, or quantum transport. The term encompasses theoretical and experimental frameworks where thermal effects are governed by potentials linked to the physical mechanisms—be it superconducting gap asymmetry, matter-enhanced neutrino propagation, thermal gauge fields in quantum transport, or temperature-dependent phenomena in neuronal signaling and device engineering. NSI thermal potentials manifest as effective terms in Hamiltonians, circuit equations, or quantum kinetic equations, and serve as critical tunable parameters for optimizing device performance, constraining new physics, and elucidating non-equilibrium effects in diverse nanoscale and quantum environments.

1. Theoretical Formulation of NSI Thermal Potentials

NSI thermal potentials arise as additional terms in the governing equations for transport, energy exchange, or quantum dynamics:

• In superconducting tunnel devices (e.g., NIS, SINIS junctions), thermal potentials are modeled using self-consistent electrical and thermal circuit equations. For the SINIS structure, the current and cooling power are determined by integrals over the density of states, with temperature-dependent terms incorporated via the Dynes parameter $\Gamma$ and the superconducting gap $\Delta(T_S)$ (Chaudhuri et al., 2011).
• In neutrino physics, NSI thermal potentials modify the matter Hamiltonian governing oscillations. The standard matter term is augmented by NSI parameters $\epsilon_{\alpha\beta}$:

$$H = \frac{1}{2E} \left[ U\,\text{diag}(m_1^2,\ m_2^2,\ m_3^2) U^\dagger + a \cdot M_\text{NSI} \right]$$

where $a = 2\sqrt{2}G_F N_e E$ and $M_\text{NSI}$ includes all $\epsilon_{\alpha\beta}$ couplings (Bakhti et al., 2020, Devi et al., 28 Dec 2024, Konwar et al., 7 Jul 2025).

• In quantum transport, NSI thermal potentials originate from temperature-dependent four-dimensional damping forces in the quantum Boltzmann equation (QBE), which are related to emergent thermal scalar and vector gauge potentials (Wang, 17 Jul 2025):

$$\nabla \cdot A = F_\text{damp,1},\qquad \partial_t \psi = F_\text{damp,2}$$

where $A$ and $\psi$ encode the vector and scalar components of the damping force induced by electron-phonon interaction.

• For neuronal microdomains, thermal potentials are linked to the voltage profile in confined dielectric geometries obeying modified Liouville–Gelfand–Bratley (LGB) equations with non-absorbing boundary conditions (Lichtervelde et al., 2019).

These formulations highlight that NSI thermal potentials encode both medium-induced modifications and non-ideal device or system properties critical for real-world behavior and applications.

2. Device-Level Phenomena: NIS/SINIS Junctions and Thermal Transistors

NSI thermal potentials play a foundational role in mesoscopic and cryogenic devices founded on normal metal–superconductor interfaces:

• Asymmetric SINIS Junctions: Device performance—cooling power, conductance, and thermometric sensitivity—is determined by self-consistently solving circuit equations for voltage drops across asymmetric junctions ($R_L \neq R_R$) and including the NSI-related thermal potentials through heat current and electron-phonon coupling terms. Asymmetry generates excess subgap current, negative differential resistance (NDR), and improves maximum cooling power, sometimes by over 200% with strong resistance differences (Chaudhuri et al., 2011).
• Thermal Transistor Functionality: In three-terminal NS junctions, NSI thermal potentials arise via temperature-dependent superconducting gaps. The negative differential thermal conductance (NDTC) effect allows amplification of thermal current, with tunability via quantum dot levels and coupling strengths:

$$\beta_h^L = \left| \frac{G_{hL}}{G_{hL}+G_{hR}} \right|$$

where $G_{h\alpha}$ is the differential thermal conductance with respect to the superconducting base temperature (Tang et al., 2018).

• Photon-Mediated NDTC and NISIN Reservoirs: In NIS junctions, photon-mediated heat exchange defines NSI thermal potential effects, measurable as NDTC under temperature-dependent impedance matching:

$$J_\gamma(T_L,T_R) = \int_0^\infty \frac{\hbar\omega}{2\pi} \tau_{LR}(\omega)\,\left[n_L(\omega) - n_R(\omega)\right] d\omega$$

NDTC emerges as negative $\partial J_\gamma/\partial T_R$ under specific material and geometric conditions (Pioldi et al., 20 Mar 2025).

• Thermoelectric Cooling and Figure of Merit: In $\alpha$-$T_3$ NIS junctions, NSI thermal potentials determine oscillatory conductance and Seebeck coefficient features, with gate-voltage-dependent behavior distinguishing optimal device operation in graphene versus dice lattice configurations (2209.06021).

The practical realization of NSI-induced thermal potentials enables optimized cooling, enhanced thermometry, and advanced thermal logic in cryogenic and nanoscale systems.

3. NSI Thermal Potentials in Neutrino Physics

In neutrino oscillation experiments and astrophysical environments, NSI thermal potentials modify neutrino propagation:

• Hamiltonian Modification: The thermal potential felt by neutrinos is expressed via both vector and scalar NSI parameters, which modify the matter effect term in the Hamiltonian. Scalar NSI contribute to the mass term with a matter density-dependent correction:

$$\delta M = S_m \begin{bmatrix} \eta_{ee} & \eta_{e\mu} & \eta_{e\tau} \ \eta_{e\mu}^* & \eta_{\mu\mu} & \eta_{\mu\tau} \ \eta_{e\tau}^* & \eta_{\mu\tau}^* & \eta_{\tau\tau} \end{bmatrix}$$

The matter dependence is analogous to thermal potentials as the effect scales linearly with density (Devi et al., 28 Dec 2024).

• Experimental Sensitivity: Next-generation long-baseline experiments (DUNE, T2HK, JUNO, HK, KNO) are sensitive to NSI parameters via appearance and disappearance channels. Off-diagonal NSI parameters ($\epsilon_{e\mu}, \epsilon_{e\tau}$) notably modify appearance probabilities, directly affecting quantum entanglement calculations (EOF, Concurrence, Negativity), particularly with prominent DUNE sensitivity near oscillation maxima (Bakhti et al., 2020, Konwar et al., 7 Jul 2025).
• Implications in Dense Media: The scaling of NSI-induced thermal potentials with ambient matter density is directly relevant for solar, supernova, or early universe environments, broadly impacting neutrino flavor evolution and the interpretation of CP-violation and mass ordering (Devi et al., 28 Dec 2024).

These findings connect NSI thermal potentials with fundamental tests of neutrino properties, including mass ordering and new physics searches.

4. Quantum Transport and Thermal Gauge Potentials

The concept of NSI thermal potentials encompasses emergent gauge fields in quantum kinetic theory:

• QBE Formulation: Electron–phonon scattering leads to a temperature-dependent, four-dimensional damping force derived via Taylor expansion of the self-energy in the quantum Boltzmann equation. This force is separated into spatial ($F_\text{damp,1}$) and scalar ($F_\text{damp,2}$) components identified as thermal vector and scalar gauge potentials:

$\nabla \cdot A = F_\text{damp,1}$

$\partial_t \psi = F_\text{damp,2}$

These potentials act analogously to electromagnetic fields and appear naturally as power/energy input terms in the transport equations (Wang, 17 Jul 2025).

• Order-by-Order Solution and Observables: The QBE is solved order by order (via Fourier transforms) in deviations from local equilibrium. The resultant distribution function corrections yield temperature-dependent current densities and reveal that the magnitude of the damping force (and thus the associated thermal potentials) increases with temperature.
• Physical Consequences: The presence of the thermal scalar potential introduces new dissipative mechanisms and modifies transport coefficients, linking NSI thermal potential theory both to established approaches (such as Luttinger’s) and novel regimes in quantum current control.

This formalism provides a rigorous underpinning to the role of temperature gradients as "gauge fields," tightly integrating NSI thermal potential effects into modern quantum transport theory.

5. Biological Systems: NSI Thermal Potentials in Neurodynamics

NSI thermal potentials also arise in biophysical contexts, notably in models where thermal and electrical phenomena interact:

• Nervous Conduction: In neuronal signaling, the action potential's thermal signature—measured as heat production and absorption—is governed by membrane electrostatics and surface charge asymmetries. Revised condenser theory employing modified LGB equations demonstrates that the internal voltage profile in dendritic microdomains (modeled as dielectric spheres) is determined by repulsive boundary conditions and an asymptotic logarithmic scaling of the potential drop with charge, replacing the classical linear dependence (Lichtervelde et al., 2019).
• Thermal Mechanisms in Neuromorphic Circuits: In VO$_2$-based neuromorphic models, temperature acts as an analogue of membrane potential, and synaptic summation is mediated by interference of thermal pulses. The threshold for switching—determined by Joule heating and external voltage bias—defines a tunable NSI thermal potential for spiking behavior, enabling dense and 3D-integrable device architectures (Velichko et al., 2019).

These NSI thermal effects establish a direct link between collective bioelectrical phenomena and generalized thermal potential models, with implications for biological signal processing and neuromorphic engineering.

6. Impact, Optimization, and Experimental Realization

The significance of NSI thermal potentials spans device optimization, new-physics searches, and advanced thermal management:

• Optimization in Devices: Fine-tuning junction asymmetry, gate voltages, fictitious gauge fields, or interface parameters enhances thermoelectric performance, maximizes cooling power, and offers robust thermal amplification or switching (Chaudhuri et al., 2011, Tang et al., 2018, Hijano et al., 2023, 2209.06021).
• Experimental Verification: Empirical studies using Al-based SINIS and NIS junctions, silver and InAs normal metals, and tailored heating/cooling experiments have validated theoretical predictions, such as excess subgap current and NDTC (Chaudhuri et al., 2011, Pioldi et al., 20 Mar 2025).
• Quantum Information and Beyond Standard Model Physics: NSI-induced thermal potentials are central to neutrino mass ordering studies and CP-violation diagnostics, with quantum entanglement measures now employed to probe NSI effects with high sensitivity in experiments such as DUNE (Konwar et al., 7 Jul 2025).
• Unified Frameworks: Thermal gauge potentials derived from the QBE provide a unified, microscopically founded description for thermal transport phenomena, connecting disparate physical systems under a common theoretical banner (Wang, 17 Jul 2025).

Pursuing NSI thermal potentials—whether in superconducting microelectronics, quantum kinetic theory, biological membranes, or high-energy physics—offers direct pathways to technological and scientific advancement, refined device control, and a deepened understanding of the interplay between thermal, electrical, and quantum effects in complex media.