Quantum effects in thermodynamics: Exploring the limitations and the potential for applications

• Applicant: Dr. Rodrigo Gallego
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Theoretical Condensed Matter Physics
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 287022405

• Final Report Year: 2021

Final Report Abstract

The field of Quantum Thermodynamics has seen a rapid development in the last years partly due to the use of mathematical techniques and conceptual insights borrowed from the field of Quantum Information Theory. In this project we have focused on three major research questions: i) provide theoretical justification for equilibration of systems and its description in terms of statistical ensembles, ii) advance the project of deriving fundamental bounds and laws of thermodynamics within the framework of a Resource Theory and iii) analyze the performance of quantum machines while including realistic limitations which arise as a consequence of dealing with small systems. The publications cover the field of quantum thermodynamics from its most applied questions – local and strong-coupling restrictions – to aspects related with the foundations of statistical mechanics. A future research direction of interest that the above question suggest is that of incorporating systems which do not equilibrate – for instance manybody localized systems – as resources for thermodynamical tasks. A promising research direction is also given by the analysis of absolutezero cooling. The bounds presented are a proof of principle of the third law of thermodynamics, but tighter and more insightful bounds are expected when introducing realistic limitations to the cooling process.

Publications

• Axiomatic characterization of the quantum relative entropy and free energy. Entropy 19, 241 (2017)
  H. Wilming, R. Gallego and J. Eisert
  
• Third law of Thermodynamics as a single inequality. Phys. Rev. X 7, 041033 (2017)
  H. Wilming and R. Gallego
  
• Quantum thermodynamics with local control. Phys. Rev. E 97, 022142 (2018)
  J. Lekscha, H. Wilming, J. Eisert and R. Gallego
  
• Statistical ensembles without tipicality. Nat. Comm. 9, 1022 (2018)
  P. Boes, H. Wilming, J. Eisert and R. Gallego
  
• Strong coupling corrections in Quantum Thermodynamics. Phys. Rev. Lett. 120, 120602 (2018)
  M. Perarnau- Llobet, H. Wilming, A. Riera, R. Gallego and J. Eisert
  
• What it takes to avoid equilibration. Phys. Rev. A 98, 022135 (2018)
  R. Gallego, H. Wilming, J. Eisert and C. Gogolin
  
• Von Neumann entropy from Unitarity. Phys. Rev. Lett 122, 210402 (2019)
  P. Boes, J. Eisert, R. Gallego, M. P. Müller and H. Wilming
  
• By-passing fluctuation theorems. Quantum 4, 231 (2020)
  P. Boes, R. Gallego, N. H. Y. Ng, J. Eisert and H. Wilming