Development of an Operational Approach to Quantum Thermodynamics

• Project/Area Number: 23540448
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Mie University
• Principal Investigator: ABE Sumiyoshi 三重大学, 工学(系)研究科(研究院), 教授 (70184215)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 量子熱力学 / 正値演算子値測度 / オペレーショナル・アプローチ

Research Abstract

The results obtained in this research project are classified into two categories. One was to clarify the physical properties of the quantum-mechanical analog of the Carnot cycle constructed based on the structural similarity/dissimilarity between quantum mechanics and thermodynamics. The other was to find a new case in which the Clausius inequality may be challenged, by describing thermodynamic processes in terms of non-unitary completely-positive quantum operations.

Research Products

• [Journal Article] Completely-positive quantum operations generating thermostatistical states : Comparative study (2014)
  • Author(s): Y. Matsuo and S. Abe
  • Journal Title: Physica A Volume: (掲載決定)
  • Peer Reviewed
• [Journal Article] Fokker-Planck theory of nonequilibrium systems governed by hierarchical dynamics (2014)
  • Author(s): S. Abe
  • Journal Title: Foundations of Physics Volume: Vol.44 Pages: 175-182
  • Peer Reviewed
• [Journal Article] Variational principle for fractional kinetics and Lévy Ansatz (2013)
  • Author(s): S. Abe
  • Journal Title: Physical Review E Volume: Vol.88 Pages: 22142-22142
  • Peer Reviewed
• [Journal Article] General formula for the efficiency of quantum-mechanical analog of the Carnot engine (2013)
  • Author(s): S. Abe
  • Journal Title: Entropy Volume: Vol.15 Pages: 1408-1415
  • Peer Reviewed
• [Journal Article] Variational principle for fractional kinetics and Levy Ansatz (2013)
  • Author(s): S. Abe
  • Journal Title: Physical Review E Volume: 88 Pages: 22142-22142
  • Peer Reviewed
• [Journal Article] Dynamical evolution of the community structure of complex earthquake network (2012)
  • Author(s): S. Abe and N. Suzuki
  • Journal Title: EPL Volume: Vol.99 Pages: 39001-39001
  • Peer Reviewed
• [Journal Article] Thermodynamic processes generated by a class of completely positive quantum operations (2012)
  • Author(s): S. Abe and Y. Aoyaghi
  • Journal Title: International Journal of Modern Physics B Volume: Vol.26 Pages: 1241001-1241001
  • Peer Reviewed
• [Journal Article] Aftershocks in Modern Perspectives : Complex Earthquake Network, Aging, and Non-Markovianity (2012)
  • Author(s): S. Abe and N. Suzuki
  • Journal Title: Acta Geophysica Volume: Vol.60 Pages: 547-561
  • Peer Reviewed
• [Journal Article] Universal law for waiting internal time in seismicity and its implication to earthquake network (2012)
  • Author(s): S. Abe and N. Suzuki
  • Journal Title: EPL Volume: Vol.97 Pages: 49002-49002
  • Peer Reviewed
• [Journal Article] On the Geodesic Nature of Wegner's Flow (2012)
  • Author(s): Y. Itto and S. Abe
  • Journal Title: Foundations of Physics Volume: Vol.42 Pages: 377-387
  • Peer Reviewed
• [Journal Article] Role of the superposition principle for enhancing the efficiency of the quantum-mechanical Carnot engine (2012)
  • Author(s): S. Abe and S. Okuyama
  • Journal Title: Physical Review E Volume: Vol.85 Pages: 11104-11104
  • Peer Reviewed
• [Journal Article] On the Geodesic Nature of Wegner’s Flow (2012)
  • Author(s): Y. Itto and S. Abe
  • Journal Title: Foundations of Physics Volume: 42 Issue: 3 Pages: 377-387
  • DOI: 10.1007/s10701-011-9606-8
  • Peer Reviewed
• [Journal Article] Aftershocks in Modern Perspectives: Complex Earthquake Network, Aging, and Non-Markovianity (2012)
  • Author(s): S. Abe and N. Suzuki
  • Journal Title: Acta Geophysica Volume: 60 Issue: 3 Pages: 547-561
  • DOI: 10.2478/s11600-012-0026-8
  • Peer Reviewed
• [Journal Article] Necessary and Sufficient Condition for Stability of Generalized Expectation Value (2011)
  • Author(s): A. El Kaabouchi and S. Abe
  • Journal Title: Journal of Applied Mathematics Pages: 804836-804836
  • Peer Reviewed
• [Journal Article] Gauge fields and geometric control of quantum-thermodynamic engine (2011)
  • Author(s): S. Abe
  • Journal Title: Journal of Statistical Mechanics : Theory and Experiment Pages: 9011-9011
  • Peer Reviewed
• [Journal Article] Maximum-power quantummechanical Carnot engine (2011)
  • Author(s): S. Abe
  • Journal Title: Physical Review E Volume: Vol.83 Pages: 41117-41117
  • Peer Reviewed
• [Journal Article] Similarity between quantum mechanics and thermodynamics: entropy, temperature, and Carnot cycle (2011)
  • Author(s): S. Abe and S. okuyama
  • Journal Title: Physical Review E Volume: 83 Pages: 21121-21121
  • Peer Reviewed
• [Journal Article] Maximum-power quantum-mechanical Carnot engine (2011)
  • Author(s): S. Abe
  • Journal Title: Physical Review E Volume: 83 Pages: 41117-41117
  • Peer Reviewed
• [Journal Article] Gauge fields and geometric control of quantum-thermodynamic engine (2011)
  • Author(s): S. Abe
  • Journal Title: Journal of Statistical Mechanics: Theory and Experiment Volume: no volume number
  • Peer Reviewed
• [Journal Article] Necessary and sufficient condition for stability of generalized expectation value (2011)
  • Author(s): A. El Kaabouchi and S. Abe
  • Journal Title: Journal of Applied Mathematics Volume: no volume number Pages: 804836-804836
  • Peer Reviewed
• [Presentation] Quantum-Mechanical Analog of the Carnot Cycle : General Formula for Efficiency and Maximum-Power Output (2013)
  • Author(s): S. Abe
  • Organizer: The 12th Joint European Thermodynamics Conference
  • Place of Presentation: Brescia, Italy
  • Invited
• [Presentation] Quantum-Mechanical Analog of the Carnot Cycle: General Formula for Efficiency and Maximum-Power Output (2013)
  • Author(s): S. Abe
  • Organizer: The 12th Joint European Thermodynamics Conference
  • Place of Presentation: Brescia, Italy
  • Invited
• [Presentation] Kinetic Theory of Superstatistics (2012)
  • Author(s): S. Abe
  • Organizer: The 3rd International Workshop on Statistical Physics and Mathematics for Complex Systems
  • Place of Presentation: Kazan, Russia
  • Invited
• [Presentation] Kinetic Theory of Superstatistics (2012)
  • Author(s): S. Abe
  • Organizer: The 3rd International Workshop on Statistical Physics and Mathematics for Complex Systems
  • Place of Presentation: Kazan大学（ロシア）
  • Invited
• [Presentation] Gauge-Theoretic Structure in Quantum Thermodynamics (2011)
  • Author(s): S. Abe
  • Organizer: International Conference on Statistical Physics-SigmaPhi2011
  • Place of Presentation: Larnaca, Cyprus
  • Invited
• [Presentation] Gauge-theoretic structure in quantum thermodynamics (2011)
  • Author(s): S. Abe
  • Organizer: International Conference on Statistical Physics-SigmaPhi2011(招待講演)
  • Place of Presentation: Larnaca (Cyprus)
• [Book] Proceedings of "The 3rd International Workshop on Statistical Physics and Mathematics for Complex Systems", Journal of Physics : Conference Series Vol. 394 (2012)
  • Author(s): D. Tayurskii, S. Abe, and Q. A. Wang 編著
• [Remarks] 目下、作成中。