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Optimal Condition of Quantum Maxwell's Demon for Maximizing Reversibility

This research explores the optimal condition of the quantum Maxwell's demon, a thought experiment that violates the second law of thermodynamics. The study aims to maximize reversibility by optimizing work, expansion, insertion, and measurement processes. The physical meaning of the optimal condition and its relationship to Casimir-like forces are also examined.

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Optimal Condition of Quantum Maxwell's Demon for Maximizing Reversibility

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  1. Sang Wook Kim (Pusan N. Univ) Optimal condition of Q-SZE Busan (2015.11.28)

  2. Collaborators Simone de Liberato (Univ. of Southampton) Hee Jun Jeon (PNU) Takahiro Sagawa (Univ. of Tokyo) Jung Jun Park (Singapore Natl. U.) Masahito Ueda (Univ. of Tokyo) Kang-Hwan Kim (KAIST)

  3. Maxwell’s Demon Now let us suppose … that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the 2nd law of thermodynamics. - J. C. Maxwell (1871)

  4. Szilard’s engine(1929) T

  5. Quantum Maxwell’s demon?

  6. Thermodynamic work in Q-world T q-thermodynamic heat in equilibrium q-thermodynamic work partition function Kieu, PRL (2004)

  7. Inserting a wall Inserting a wall is considered as an isothermal process.

  8. Adiabatic process for inserting a wall T should be changed quantum adiabatic The final state should be in non-equilibrium, so that the irreversible process inevitably occurs in isothermal expansion.

  9. Q-work in an isothermal process Helmholtz free energy difference (Note) Due to isothermal process, we don’t have to consider a full density matrix.

  10. Thermodynamic process Expansion T Removal Insertion T T Measurement

  11. Q-work of q-Szilard engine SWK, Sagawa, De Liberato & Ueda, PRL (2011)

  12. Single particle q-Szilard engine The 3rd law of thermodynamics K.-H. Kim & SWK, J. Korean Phys. Soc. (2012)

  13. Two particle q-Szilard engine I

  14. Two particle q-Szilard engine II Bosons Fermions (spinless) Both and are prohibited due to Pauli exclusion principle in the low T. (cf) classical work

  15. Two particle q-Szilard engine III ( =1/2) Bosons Classical Fermions SWK, Sagawa, De Liberato & Ueda, PRL (2011)

  16. Two particle q-Szilard engine IVwith varying Fermions Bosons K.-H. Kim & SWK, J. Korean Phys. Soc. (2012)

  17. Irreversible process I Time-forward Time-backward Inherently irreversible! (cf) Murashita, Funo & Ueda, PRE (2014) Ashida, Funo, Murashita & Ueda, PRE (2014)

  18. Irreversible process II-relaxation

  19. “A reversible heat engine has the maximum efficiency.”- Carnot

  20. (Option 1) Make the protocol reversible Horowitz & Parrond, NJP (2011)

  21. (Option 2) Optimize work Expansion Insertion T Measurement

  22. Maximizing reversibility Optimal condition Reversibility

  23. Physical meaning of optimal condition Time-backward Time-forward

  24. Numerical check I

  25. Numerical check II

  26. Casimir-like force? Why? Time-backward

  27. How about Two spinless fermions

  28. The optimal condition of the q-SZE with intrinsic irreversibility is achieved once the reversibility is maximized.

  29. K.-H. Kim & SWK, J. Korean Phys. Soc. (2012)

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