2210.14057
Time–Varying Capacitors as Lossless Two–Port Devices
Dimitri Jeltsema
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper models the time-varying capacitor as a two-port with state equations Q̇=I and Ċ=U, outputs V=Q/C and F=−Q^2/(2C^2), and storage S(Q,C)=Q^2/(2C). It explicitly derives the power balance dS/dt=VI+FU (its eq. (24)) and concludes the device is passive and, in fact, lossless as a two-port, exactly matching the candidate’s chain-rule proof and conclusion, assuming C(t)>0 so S≥0 . The passivity/losslessness notion used is the standard one (Appendix eq. (34)), so integrating yields S(t2)−S(t1)=∫(VI+FU)dt, again in line with the candidate solution . The arguments agree step-for-step; no discrepancy was found.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper’s two-port modeling resolves the apparent thermodynamic inconsistency of one-port formulations for time-varying capacitors and provides a clean, correct energy balance. The derivation of dS/dt=VI+FU and the conclusion of (in fact) losslessness are straightforward and sound. Minor revisions would make assumptions explicit and further bridge the abstraction to physical mechanisms.