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Conservation of Mass in Finite Cotrol Volume01:16

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The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
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Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium.
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Violation of Detailed Balance in Quantum Open Systems.

Robert Alicki1, Milan Šindelka2, David Gelbwaser-Klimovsky3

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We show that quantum systems in a dilute gas can exhibit persistent currents at thermal equilibrium. This occurs because detailed balance can be violated, allowing for continuous probability and heat flow.

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Area of Science:

  • Quantum thermodynamics
  • Quantum statistical mechanics
  • Condensed matter physics

Background:

  • Understanding quantum system dynamics in thermal environments is crucial.
  • Quantum Markovian master equations describe open quantum systems.
  • The low-density limit simplifies complex gas-system interactions.

Purpose of the Study:

  • To investigate quantum system dynamics in a dilute gas at equilibrium.
  • To explore the conditions for detailed balance violation.
  • To identify novel thermalization mechanisms.

Main Methods:

  • Derivation of a quantum Markovian master equation using the low-density limit.
  • Analysis of the stationary states and detailed balance conditions.
  • Application to a model of electron hopping between quantum dots in a magnetic field.

Main Results:

  • The Gibbs state at bath temperature is always stationary.
  • Detailed balance can be violated beyond the Born approximation.
  • Absence of time-reversal symmetry in the scattering T matrix leads to persistent currents.

Conclusions:

  • A new thermalization mechanism allows persistent probability and heat currents at equilibrium.
  • Violation of detailed balance is key to this phenomenon.
  • The quantum dot model demonstrates this effect in a realistic scenario.