{
  "annotation_id": "15799bfd-979a-4fa2-b446-3472d2fdfd5b",
  "date_created": "2026-03-02T18:00:42.157000Z",
  "date_modified": "2026-03-02T18:00:42.157000Z",
  "file_hash": "7ddc38649a6ff0b30a377148e57010d0a695de711006d57ea3052463faea4860",
  "private": false,
  "record": {
    "abstract": "A thermodynamic analysis of the harmonic oscillator is presented. Motivation\nfor the study is provided by the blackbody radiation spectrum; when blackbody\nradiation is regarded as a system of noninteracting harmonic oscillator modes,\nthe thermodynamics follows from that of the harmonic oscillators. Using the\nbehavior of a harmonic oscillator thermodynamic system under a quasi-static\nchange of oscillator frequency w, we show that the thermodynamic functions can\nall be derived from a single function of w/T, analogous to Wien\u0027s displacement\ntheorem. The high- and low-frequency energy limits allow asymptotic energy\nforms involving T alone or w alone, corresponding to energy equipartition and\nzero-point energy. It is noted that the Planck spectrum with zero-point\nradiation corresponds to the function satisfying the Wien displacement result\nwhich provides the smoothest possible interpolation between energy\nequipartition at low frequency and zero-point energy at high frequency.",
    "arxiv_id": "physics/0210128",
    "authors": [
      "Timothy H. Boyer"
    ],
    "categories": [
      "physics.class-ph",
      "physics.gen-ph"
    ],
    "doi": "10.1119/1.1566782",
    "journal_ref": "Am. J. Phys. 71, 866-870 (2003).",
    "title": "Thermodynamics of the Harmonic Oscillator: Wien\u0027s Displacement Law and   the Planck Spectrum",
    "url": "https://arxiv.org/abs/physics/0210128"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2c435209-cf88-414a-bdd0-5b5e10dc9f60",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}