{
  "id": "2011.08020",
  "version": "v1",
  "published": "2020-11-16T15:16:13.000Z",
  "updated": "2020-11-16T15:16:13.000Z",
  "title": "Resource theory of heat and work with non-commuting charges: yet another new foundation of thermodynamics",
  "authors": [
    "Zahra Baghali Khanian",
    "Manabendra Nath Bera",
    "Arnau Riera",
    "Maciej Lewenstein",
    "Andreas Winter"
  ],
  "categories": [
    "quant-ph",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We consider asymptotically many non-interacting systems with multiple conserved quantities or charges. We generalize the seminal results of Sparaciari, Oppenheim and Fritz [\\emph{Phys. Rev. A} 96:052112, 2017] to the case of multiple, in general non-commuting charges. To this aim we formulate a resource theory of thermodynamics of asymptotically many non-interacting systems with multiple conserved quantities or charges. To any quantum state, we associate a vector with entries of the expected charge values and entropy of that state. We call the set of all these vectors the phase diagram of the system, and show that it characterizes the equivalence classes of states under asymptotic unitary transformations that approximately conserve the charges. Using the phase diagram of a system and its bath, we analyze the first and the second laws of thermodynamics. In particular, we show that to attain the second law, an asymptotically large bath is necessary. In the case that the bath is composed of several identical copies of the same ``elementary bath'', we quantify exactly how large the bath has to be to permit a specified work transformation of a given system, in terms of the number of copies of the elementary bath system per work system (bath rate). In particular, if the bath is relatively small, we show that the quantum setting requires an extended phase diagram exhibiting negative entropies. This corresponds to the purely quantum effect that at the end of the process, system and bath are entangled, thus permitting classically impossible transformations (unless the bath is enlarged). For a large bath, or many copies of the same elementary bath, system and bath may be left uncorrelated and we show that the optimal bath rate, as a function of how tightly the second law is attained, can be expressed in terms of the heat capacity of the bath.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-16T15:16:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "resource theory",
      "non-commuting charges",
      "second law",
      "thermodynamics",
      "elementary bath"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}