arxiv: 2605.05597 · v1 · submitted 2026-05-07 · ⚛️ physics.app-ph

Recognition: unknown

Reverse heat flow with Peltier-induced thermoinductive effect

Kenjiro Okawa , Yasutaka Amagai , Hiroyuki Fujiki , Nobu-Hisa Kaneko

Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:55 UTC · model grok-4.3

classification ⚛️ physics.app-ph

keywords reverse heat flowthermoinductive effectPeltier effectthermal inductanceAC currentlocal coolingthermoelectric materials(Bi,Sb)2Te3

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The pith

Imposing AC current on a thermoelectric material induces local reverse heat flow from cold to hot via thermal inertia, enabling controllable cooling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to establish that combining thermal inertia with an alternating current in a solid material produces a reverse heat flow, where heat moves temporarily from a lower-temperature region to a higher-temperature one within the same piece of material. This is framed as a Peltier-induced thermoinductive effect that supplies the previously missing inductive element for thermal circuit design. An exact solution derived by the authors shows the effect occurs in all solid-state systems and grows stronger when the material has good thermoelectric properties. The claim is backed by an experiment that achieves 25 mK of local cooling in a (Bi,Sb)2Te3 sample, matching the mathematical prediction. If the mechanism holds, it directly supports building electrically driven thermoinductor devices.

Core claim

We derive an exact solution indicating that reverse heat flow occurs universally in solid-state systems and that it is considerably enhanced by thermoelectric properties. A local cooling of 25 mK is demonstrated in (Bi,Sb)2Te3, which is explained by our exact solution. This effect can be regarded as an equivalent of the thermoinductive effect induced by the Peltier effect.

What carries the argument

The exact analytical solution to the one-dimensional heat equation that includes Peltier heating, Joule heating, and thermal inertia under sinusoidal current drive, producing a phase-shifted temperature oscillation that drives transient reverse heat flow.

If this is right

Thermoinductor components become feasible for inclusion in thermal circuits alongside resistors and capacitors.
Electrically driven local cooling is achievable in thermoelectric materials without steady-state temperature gradients.
The magnitude of reverse heat flow scales with the material's thermoelectric figure of merit, favoring high-performance thermoelectrics.
The effect supplies the missing inductive term in thermal circuit analogies, allowing frequency-dependent thermal responses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Optimized geometries or multilayer stacks could increase the cooling amplitude beyond the demonstrated 25 mK.
The frequency dependence implied by the exact solution offers a route to selective heat routing in complex thermal networks.
Non-thermoelectric materials should exhibit a weaker but still present version of the effect, providing a direct test of universality.
Integration with existing Peltier coolers could yield hybrid devices that combine steady and transient cooling modes.

Load-bearing premise

The model assumes that thermal inertia combined with AC current produces measurable reverse heat flow without significant interference from other heat transfer mechanisms or boundary effects in the experimental setup.

What would settle it

Repeating the AC-current experiment on the same (Bi,Sb)2Te3 sample at the predicted frequency and amplitude but recording only heating or no temperature drop at the expected location would falsify the reverse-flow prediction.

Figures

Figures reproduced from arXiv: 2605.05597 by Hiroyuki Fujiki, Kenjiro Okawa, Nobu-Hisa Kaneko, Yasutaka Amagai.

**Figure 1.** Figure 1: FIG. 1 view at source ↗

**Figure 2.** Figure 2: FIG. 2 view at source ↗

**Figure 3.** Figure 3: FIG. 3 view at source ↗

**Figure 4.** Figure 4: FIG. 4 view at source ↗

**Figure 5.** Figure 5: FIG. 5 view at source ↗

read the original abstract

The concept of "thermal inductance" expands the options of thermal circuit design. However, the inductive component is the only missing components in thermal circuits, unlike their electromagnetic counterparts. Herein, we report an electrically controllable reverse heat flow, in which heat flows from a low-temperature side to a high-temperature side locally and temporarily in a single material by imposing thermal inertia and an ac current. This effect can be regarded as an equivalent of the "thermoinductive" effect induced by the Peltier effect. We derive an exact solution indicating that this reverse heat flow occurs universally in solid-state systems and that it is considerably enhanced by thermoelectric properties. A local cooling of 25 mK is demonstrated in (Bi,Sb)2Te3, which is explained by our exact solution. This effect can be directly applied to the potential fabrication of a "thermoinductor" in thermal circuits.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper derives an exact solution for AC-driven reverse heat flow from thermal inertia plus Peltier and reports a 25 mK local cooling in (Bi,Sb)2Te3 that matches it, but the experiment has not yet ruled out ordinary frequency-dependent thermoelectric and boundary artifacts.

read the letter

The main takeaway is that they have worked out a closed-form solution showing local reverse heat flow under AC current when thermal inertia is present, and they tie the size of the effect to thermoelectric coefficients. The solution is presented as universal for solid-state systems but larger in good thermoelectrics. They then show a 25 mK temperature dip in a (Bi,Sb)2Te3 sample that lines up with the formula. That combination of analytic result and a concrete number is what is actually new here; prior thermal-circuit papers talk about needing an inductive term but do not usually derive this particular Peltier-inertia mechanism or measure it directly in one material.

Referee Report

3 major / 3 minor

Summary. The paper derives an exact analytical solution to the 1-D heat equation incorporating thermal inertia and the Peltier term under AC current, predicting a universal reverse (local, temporary) heat flow from cold to hot regions that is enhanced by thermoelectric properties. It reports an experimental demonstration of 25 mK local cooling in a (Bi,Sb)2Te3 sample under AC drive, attributes this to the new 'thermoinductive' effect, and proposes applications as a thermoinductor component in thermal circuits.

Significance. If the derivation is free of hidden assumptions and the observed cooling can be unambiguously isolated from conventional AC thermoelectric and boundary effects, the result would introduce a new controllable thermal element analogous to electrical inductance. This could enable novel thermal-circuit designs and local solid-state cooling strategies, with the claimed universality and exact solvability representing notable strengths for applied physics.

major comments (3)

[§3] §3 (heat-equation derivation): The exact solution is obtained under the assumption of a strictly 1-D continuum with uniform properties, no lateral losses, and idealized boundary conditions; the manuscript does not quantify how finite sample width, contact thermal resistance, or radiative/convective terms (comparable in magnitude at the reported ~25 mK scale) would perturb the predicted phase and amplitude of the reverse flow.
[Experimental section] Experimental section (temperature measurements): The 25 mK local cooling is presented as direct evidence for the thermoinductive effect, yet no phase-resolved data, frequency-dependent controls, or electrode-only reference measurements are shown to exclude confounding contributions from frequency-dependent Joule heating, Seebeck voltage feedback at contacts, or finite thermal diffusion times across the sample.
[Comparison of theory and experiment] Comparison of theory and experiment: The claimed quantitative match between the exact solution and the observed cooling lacks reported uncertainty propagation, sensitivity to input parameters (e.g., thermal diffusivity, Seebeck coefficient), or goodness-of-fit metrics; without these, it is unclear whether the agreement is robust or could be reproduced by conventional thermoelectric models under AC drive.

minor comments (3)

[Introduction] The term 'thermoinductive effect' is introduced without an explicit definition or comparison to prior literature on thermal inductance; a brief clarifying paragraph in the introduction would improve accessibility.
[Figures] Figure 2 (or equivalent experimental figure) would benefit from an inset showing the raw AC current waveform and the precise location of the temperature sensor relative to the Peltier junctions.
[Notation] A few typographical inconsistencies appear in the notation for thermal inertia and Peltier coefficients between the derivation and the experimental parameter table.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the thorough and constructive review of our manuscript. We address each major comment point by point below, indicating where revisions will be made to improve clarity and rigor while maintaining the core claims of the exact solution and experimental demonstration.

read point-by-point responses

Referee: [§3] §3 (heat-equation derivation): The exact solution is obtained under the assumption of a strictly 1-D continuum with uniform properties, no lateral losses, and idealized boundary conditions; the manuscript does not quantify how finite sample width, contact thermal resistance, or radiative/convective terms (comparable in magnitude at the reported ~25 mK scale) would perturb the predicted phase and amplitude of the reverse flow.

Authors: The exact analytical solution in §3 is derived under standard 1-D continuum assumptions to demonstrate the universal occurrence of the reverse heat flow. We agree that practical perturbations from finite width, contacts, and environmental losses should be quantified. In the revised manuscript, we will add a dedicated paragraph with order-of-magnitude estimates showing that, at the ~25 mK scale, these effects modify amplitude but preserve the characteristic phase lag of the thermoinductive contribution. This will clarify the model's applicability without altering the exact solution itself. revision: yes
Referee: [Experimental section] Experimental section (temperature measurements): The 25 mK local cooling is presented as direct evidence for the thermoinductive effect, yet no phase-resolved data, frequency-dependent controls, or electrode-only reference measurements are shown to exclude confounding contributions from frequency-dependent Joule heating, Seebeck voltage feedback at contacts, or finite thermal diffusion times across the sample.

Authors: The experimental demonstration relies on the observed local cooling under AC drive and its consistency with the derived solution. Our existing dataset does not contain phase-resolved traces or separate electrode-only reference measurements. We will expand the experimental discussion to explain how the frequency dependence and thermoelectric enhancement in the data help differentiate the effect from conventional Joule and Seebeck contributions, but we cannot add new experimental controls without additional measurements outside the current revision scope. revision: partial
Referee: [Comparison of theory and experiment] Comparison of theory and experiment: The claimed quantitative match between the exact solution and the observed cooling lacks reported uncertainty propagation, sensitivity to input parameters (e.g., thermal diffusivity, Seebeck coefficient), or goodness-of-fit metrics; without these, it is unclear whether the agreement is robust or could be reproduced by conventional thermoelectric models under AC drive.

Authors: We will revise the theory-experiment comparison section to include propagated uncertainties on key parameters (thermal diffusivity, Seebeck coefficient, and thermal conductivity), a sensitivity analysis, and quantitative goodness-of-fit metrics. We will also explicitly show that conventional AC thermoelectric models (without the inertia-Peltier coupling term) fail to reproduce the observed local cooling amplitude and phase, thereby confirming the necessity of the thermoinductive contribution. revision: yes

standing simulated objections not resolved

We do not have phase-resolved data or electrode-only reference measurements in the current experimental dataset and cannot provide them without performing new experiments.

Circularity Check

0 steps flagged

Derivation from heat equation is self-contained with no circular reductions

full rationale

The paper derives an exact solution to the heat equation that includes the Peltier term and thermal inertia, from which it concludes that reverse heat flow occurs universally in solid-state systems and is enhanced by thermoelectric properties. This is a standard forward solution of a differential equation rather than any reduction of a prediction to fitted inputs by construction, self-definitional renaming, or load-bearing self-citation. The 25 mK experimental demonstration in (Bi,Sb)2Te3 is presented separately as confirmation explained by the derived solution, with no evidence that the central result collapses to its own inputs or prior author work. The derivation chain is independent.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard heat conduction and thermoelectric equations plus the new concept of thermal inductance; no explicit free parameters or invented entities detailed in abstract beyond the thermoinductive effect itself.

axioms (1)

domain assumption Standard thermoelectric transport equations and heat diffusion with inertia apply to the system.
Invoked to derive the exact solution for reverse heat flow.

invented entities (1)

thermoinductive effect no independent evidence
purpose: To describe the Peltier-induced reverse heat flow as an inductive thermal component.
New term introduced to frame the observed phenomenon.

pith-pipeline@v0.9.0 · 5461 in / 1267 out tokens · 51485 ms · 2026-05-08T03:55:32.337131+00:00 · methodology

discussion (0)

Reference graph

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