{
  "id": "2212.07024",
  "version": "v1",
  "published": "2022-12-14T04:36:09.000Z",
  "updated": "2022-12-14T04:36:09.000Z",
  "title": "Generalized energy equipartition in electrical circuits",
  "authors": [
    "Aritra Ghosh"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "In this brief note, we demonstrate a generalized energy equipartition theorem for a generic electrical circuit with Johnson-Nyquist (thermal) noise. From quantum mechanical considerations, the thermal modes have an energy distribution dictated by Planck's law. For a resistive circuit with some inductance, it is shown that the real part of the admittance is proportional to a probability distribution function which modulates the contributions to the system's mean energy from various frequencies of the Fourier spectrum. Further, we analyze the case with a capacitor connected in series with an inductor and a resistor. The results resemble superstatistics, i.e. a superposition of two statistics and can be reformulated in the energy representation. The correct classical limit is obtained as $\\hbar \\rightarrow 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-14T04:36:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized energy equipartition theorem",
      "probability distribution function",
      "systems mean energy",
      "quantum mechanical considerations",
      "thermal modes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}