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Related Concept Videos

Efficiency of The Carnot Cycle01:16

Efficiency of The Carnot Cycle

The hypothetical Carnot cycle consists of an ideal gas subjected to two isothermal and two adiabatic processes. Since the internal energy of an ideal gas depends only on its temperature, which is the same before and after the completion of the Carnot cycle, there is no change in its internal energy. Hence, using the first law of thermodynamics, the total heat exchanged by the ideal gas equals the total work done. Thus, we can quantify the efficiency of the Carnot cycle via the heat exchanged...
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Comparative Study of Simulation of Temperature Rise in Ring Main Unit
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Published on: July 5, 2024

Master equation and two heat reservoirs.

Steffen Trimper1

  • 1Institute of Physics, Martin-Luther-University, D-06099 Halle, Germany. steffen.trimper@physik.uni-halle.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
Summary

This study analyzes a spin-flip process with two heat reservoirs, revealing a generalized Fermi-Dirac distribution and a dynamically induced first-order phase transition due to temperature-dependent symmetry. This research offers insights into non-equilibrium statistical mechanics.

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Area of Science:

  • Statistical Mechanics
  • Quantum Physics
  • Condensed Matter Theory

Background:

  • Investigates spin-flip dynamics in systems with two distinct heat reservoirs.
  • Explores non-equilibrium thermodynamics and phase transitions.

Purpose of the Study:

  • To analyze a simple spin-flip process influenced by two heat baths at different temperatures (T and T').
  • To derive a generalized Fermi-Dirac distribution and understand the system's relaxation dynamics.
  • To investigate the emergence of a first-order phase transition induced by system symmetry.

Main Methods:

  • Utilizes a master equation approach within a second-quantized Hamiltonian formulation.
  • Derives the stationary solution to obtain an effective temperature (Te) and relaxation time.
  • Applies Landau expansion to the averaged spin () to derive a free energy functional.

Main Results:

  • Identifies a generalized Fermi-Dirac distribution characterized by an effective temperature (Te).
  • Establishes a relationship between relaxation time and the effective temperature.
  • Reveals a symmetry (sigma<-->-sigma and T<-->T') leading to a third-order term in free energy.
  • Demonstrates a dynamically induced first-order phase transition.

Conclusions:

  • The interplay between two heat reservoirs and spin dynamics can lead to novel thermodynamic behaviors.
  • The derived free energy functional and symmetry properties are key to understanding the induced phase transition.
  • This model provides a framework for studying non-equilibrium phase transitions in quantum systems.