Passive Self-Heating Is a Natural Equalizer: Quantitative Characterization, Capability Boundaries, and the Gain Surface of Consistency Flattening in Series Sodium-Ion Battery Packs

Problem. Cell-to-cell internal-resistance dispersion is amplified at sub-zero temperatures and is widely regarded as the root cause of pack-level capacity loss and lifetime divergence. Industry and academia converge on one idea: eliminate the dispersion—active balancing, external preheating, and stringent dual-parameter sorting. A reversed proposition has been largely overlooked: in a series string, where current is common, resistance dispersion itself drives a passive self-homogenization mechanism—the highest-resistance cell dissipates the most Joule heat, warms the most, and its resistance drops the most, so it “catches up” with its lower-resistance neighbours. Ref. [1] proved that the sign of this compression is locked solely by 𝜕R/𝜕T<0. This paper answers the follow-up questions: how much? when does it fail? is it stable in the long run? can a quantitative surface be provided to guide sorting? Contributions. Using a physics-based sandbox calibrated against published measurements (second-order RC + VTF viscosity + Arrhenius coupling + lumped thermal model including entropic heat + concentrationpolarization truncation + dual capacity/resistance dispersion), we report six results: 1. First systematic quantification: at −30 °C/0.5C the capacity COV is flattened by 39.7% (3.47%→2.09%) with mean capacity +9.9%; the high-resistance group’s capacity rises +12.2% versus +8.0% for the low-resistance group, narrowing the high–low gap by 33.9%. Results are consistent before and after completing the physical model (40.7%→39.7%), excluding a modeling artifact. 2. Capability boundary: the mechanism is a resistance corrector, not a capacity corrector—it fails (and even mildly reverses) once capacity COV reaches about 3%; yet even when flattening is marginal, mean usable capacity still rises by about 5%. 3. C-rate sweet spot: a narrow window of 0.5–0.8C with threshold activation rather than gradual enhancement (a 12.7 pp jump from 0.45C to 0.5C); at 0.8C the flattening reaches 92.4% (isothermal COV 31.7% versus thermal 2.4%) and usable capacity is recovered by a factor of 5.5; at 1.0C everything is extinguished. 4. Full-temperature applicability domain: short-term flattening decreases monotonically from 69.4% at −30 °C to zero at 40 °C—it is a low-temperature-specific tool; at room temperature cells are already highly consistent and need no flattening. 5. Long-term stability: after 500 cycles the COV has not widened at all (both groups 4.46%)—the negative feedback exactly offsets the aging positive feedback of the central cells (aging-rate ratio 1.27×). Entropy generation—the industry’s universal villain—turns out to be a benefactor in lowtemperature self-heating. 6. Gain surface 𝜂=f(COV_Q,COV_R): capacity COVcontributes 69.1%of the variance (dominant) and resistance COV 30.9%; a threefold change in resistance COV perturbs the residual COV by ≤0.06 pp—resistance dispersion is “eaten clean” by self-heating, and the residual floor is set by capacity.