Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle
Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fi...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2022-09-01
|
Series: | Entropy |
Subjects: | |
Online Access: | https://www.mdpi.com/1099-4300/24/9/1306 |
_version_ | 1797488671907119104 |
---|---|
author | Huan-Qiang Zhou Qian-Qian Shi Yan-Wei Dai |
author_facet | Huan-Qiang Zhou Qian-Qian Shi Yan-Wei Dai |
author_sort | Huan-Qiang Zhou |
collection | DOAJ |
description | Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XYZ model, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time. |
first_indexed | 2024-03-10T00:05:39Z |
format | Article |
id | doaj.art-c8edb240e5a245a8bc7b7371898fc600 |
institution | Directory Open Access Journal |
issn | 1099-4300 |
language | English |
last_indexed | 2024-03-10T00:05:39Z |
publishDate | 2022-09-01 |
publisher | MDPI AG |
record_format | Article |
series | Entropy |
spelling | doaj.art-c8edb240e5a245a8bc7b7371898fc6002023-11-23T16:09:26ZengMDPI AGEntropy1099-43002022-09-01249130610.3390/e24091306Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s PrincipleHuan-Qiang Zhou0Qian-Qian Shi1Yan-Wei Dai2Centre for Modern Physics, Chongqing University, Chongqing 400044, ChinaCentre for Modern Physics, Chongqing University, Chongqing 400044, ChinaCentre for Modern Physics, Chongqing University, Chongqing 400044, ChinaFidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XYZ model, the quantum spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.https://www.mdpi.com/1099-4300/24/9/1306quantum critical phenomenatensor network algorithmssymmetry-breaking ordertopological orderan analogue of Landauer’s principleanalogues of the four thermodynamic laws |
spellingShingle | Huan-Qiang Zhou Qian-Qian Shi Yan-Wei Dai Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle Entropy quantum critical phenomena tensor network algorithms symmetry-breaking order topological order an analogue of Landauer’s principle analogues of the four thermodynamic laws |
title | Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle |
title_full | Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle |
title_fullStr | Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle |
title_full_unstemmed | Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle |
title_short | Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle |
title_sort | fidelity mechanics analogues of the four thermodynamic laws and landauer s principle |
topic | quantum critical phenomena tensor network algorithms symmetry-breaking order topological order an analogue of Landauer’s principle analogues of the four thermodynamic laws |
url | https://www.mdpi.com/1099-4300/24/9/1306 |
work_keys_str_mv | AT huanqiangzhou fidelitymechanicsanaloguesofthefourthermodynamiclawsandlandauersprinciple AT qianqianshi fidelitymechanicsanaloguesofthefourthermodynamiclawsandlandauersprinciple AT yanweidai fidelitymechanicsanaloguesofthefourthermodynamiclawsandlandauersprinciple |