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The mechanical efficiency of a machine is a fundamental concept that describes how effectively a machine can convert input work into output work. According to this concept, the efficiency of a machine is equal to the ratio of the output work to the input work. An ideal machine, meaning a machine that has no energy losses, has an efficiency of one. This implies that the input work and the output work are equal.
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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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Efficiency of single-particle engines.

Karel Proesmans1, Cedric Driesen1, Bart Cleuren1

  • 1Faculty of Sciences, Hasselt University, B-3590 Diepenbeek, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
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This study analyzes the efficiency of single-particle engines, finding work distribution is Gaussian with corrections depending on piston speed. Numerical confirmation of efficiency fluctuations and unique zero-temperature behaviors are also presented.

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Area of Science:

  • Statistical mechanics
  • Thermodynamics
  • Quantum thermodynamics

Background:

  • The Szilard and Carnot engines are fundamental models for studying thermodynamics at the nanoscale.
  • Understanding the efficiency and work output of these engines is crucial for developing micro- and nano-scale devices.
  • Previous research has focused on quasistatic limits, but real-world applications require understanding non-equilibrium dynamics.

Purpose of the Study:

  • To investigate the efficiency of a single-particle Szilard engine and a single-particle Carnot engine.
  • To analyze the work distribution and efficiency corrections beyond the quasistatic limit.
  • To explore the stochastic efficiency and fluctuations, particularly in the zero-temperature limit.

Main Methods:

  • Theoretical analysis incorporating first-order corrections to the quasistatic limit.
  • Derivation of the work distribution for the engine models.
  • Numerical simulations to confirm theoretical predictions on efficiency fluctuations.
  • Investigation of the zero-temperature thermodynamic behavior.

Main Results:

  • The work distribution for both engine models approaches a Gaussian form within the first-order correction.
  • The correction factor for average work and efficiency is solely dependent on the piston speed.
  • Numerical results validate recent findings regarding efficiency fluctuations in stochastic thermodynamics.
  • Unique thermodynamic features emerge in the zero-temperature limit.

Conclusions:

  • The study provides a refined understanding of single-particle engine efficiency beyond equilibrium assumptions.
  • Piston speed emerges as a critical parameter influencing work and efficiency corrections.
  • The findings contribute to the field of stochastic thermodynamics by confirming fluctuation theorems numerically.
  • The zero-temperature limit reveals novel aspects of nanoscale thermodynamic processes.