skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines

Abstract

Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot{close_quote}s theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot{close_quote}s theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible {ital and irreversible} engines is shown to arise from the Ginzburg-Landau description of the broken phase. {copyright}more » {ital 1998} {ital The American Physical Society}« less

Authors:
 [1]
  1. Los Alamos National Laboratory, Earth and Environmental Sciences Division, Los Alamos, New Mexico 87545 (United States)
Publication Date:
OSTI Identifier:
641615
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Additional Journal Information:
Journal Volume: 58; Journal Issue: 3; Other Information: PBD: Sep 1998
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; HEAT ENGINES; THERMODYNAMIC CYCLES; THERMAL EFFICIENCY; ENTROPY; RESONATORS; SYMMETRY BREAKING; SCALING LAWS

Citation Formats

Smith, E, and Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029. Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines. United States: N. p., 1998. Web. doi:10.1103/PhysRevE.58.2818.
Smith, E, & Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029. Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines. United States. https://doi.org/10.1103/PhysRevE.58.2818
Smith, E, and Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029. 1998. "Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines". United States. https://doi.org/10.1103/PhysRevE.58.2818.
@article{osti_641615,
title = {Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines},
author = {Smith, E and Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78713-8029},
abstractNote = {Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot{close_quote}s theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot{close_quote}s theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible {ital and irreversible} engines is shown to arise from the Ginzburg-Landau description of the broken phase. {copyright} {ital 1998} {ital The American Physical Society}},
doi = {10.1103/PhysRevE.58.2818},
url = {https://www.osti.gov/biblio/641615}, journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 3,
volume = 58,
place = {United States},
year = {Tue Sep 01 00:00:00 EDT 1998},
month = {Tue Sep 01 00:00:00 EDT 1998}
}