Statistical mechanics of self-driven Carnot cycles

Journal Article · Fri Oct 01 04:00:00 EDT 1999 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.60.3633· OSTI ID:686870

Smith, E ^[1]

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1. Los Alamos National Laboratory, Earth and Environmental Sciences Division, Los Alamos, New Mexico 87545 (United States)

The spontaneous generation and finite-amplitude saturation of sound, in a traveling-wave thermoacoustic engine, are derived as properties of a second-order phase transition. It has previously been argued that this dynamical phase transition, called {open_quotes}onset,{close_quotes} has an equivalent equilibrium representation, but the saturation mechanism and scaling were not computed. In this work, the sound modes implementing the engine cycle are coarse-grained and statistically averaged, in a partition function derived from microscopic dynamics on criteria of scale invariance. Self-amplification performed by the engine cycle is introduced through higher-order modal interactions. Stationary points and fluctuations of the resulting phenomenological Lagrangian are analyzed and related to background dynamical currents. The scaling of the stable sound amplitude near the critical point is derived and shown to arise universally from the interaction of finite-temperature disorder, with the order induced by self-amplification. {copyright} {ital 1999} {ital The American Physical Society}

• OSTI ID: 686870
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 60; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CARNOT CYCLE
PARTITION FUNCTIONS
PHASE TRANSFORMATIONS
SCALE INVARIANCE
STATISTICAL MECHANICS