Version 1
: Received: 13 July 2021 / Approved: 14 July 2021 / Online: 14 July 2021 (11:00:21 CEST)
How to cite:
Romero-Rochin, V. Sharp Energy Self-Determination of Macroscopic Quantum Bodies in Pure States, as a Validation of the First Law of Thermodynamics. Preprints2021, 2021070319. https://doi.org/10.20944/preprints202107.0319.v1
Romero-Rochin, V. Sharp Energy Self-Determination of Macroscopic Quantum Bodies in Pure States, as a Validation of the First Law of Thermodynamics. Preprints 2021, 2021070319. https://doi.org/10.20944/preprints202107.0319.v1
Romero-Rochin, V. Sharp Energy Self-Determination of Macroscopic Quantum Bodies in Pure States, as a Validation of the First Law of Thermodynamics. Preprints2021, 2021070319. https://doi.org/10.20944/preprints202107.0319.v1
APA Style
Romero-Rochin, V. (2021). Sharp Energy Self-Determination of Macroscopic Quantum Bodies in Pure States, as a Validation of the First Law of Thermodynamics. Preprints. https://doi.org/10.20944/preprints202107.0319.v1
Chicago/Turabian Style
Romero-Rochin, V. 2021 "Sharp Energy Self-Determination of Macroscopic Quantum Bodies in Pure States, as a Validation of the First Law of Thermodynamics" Preprints. https://doi.org/10.20944/preprints202107.0319.v1
Abstract
We argue that a very large class of quantum pure states of isolated macroscopic bodies have sharply peaked energy distributions, with their width relative to the average scaling between $\sim N^{-1}$ and $\sim N^{-1/2}$, with $N \gg 1$, the number of atoms conforming the body. Those states are dense superpositions of energy eigenstates within arbitrary finite or infinite energy intervals that decay sufficiently fast. The sharpness of the energy distribution implies that closed systems in those states are {\it microcanonical} in the sense that only energy eigenstates very near to the mean energy contribute to their thermodynamic evolution. Since thermodynamics accurately describes processes of macroscopic bodies and requires that closed systems have constant energy, our claim is that these pure states are typical of macroscopic systems. The main assumption beneath the energy sharpness is that the isolated body can reach thermal equilibrium if left unaltered. We argue that such a self-sharpness of the energy in macroscopic bodies indicates that the First Law of Thermodynamics is statistical in character.
Keywords
quantum mechanics of macroscopic systems; thermodynamics; pure quantum states
Subject
Physical Sciences, Acoustics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
