Trajectory-Based Approach to Quantum Thermodynamics

  • 30 March 2022
  • 13-14
  • DAV1102

Speaker: Prof. Tapio Ala-Nissila (Loughborough University)

Title: Trajectory-Based Approach to Quantum Thermodynamics

Abstract: One of the main problems in developing a consistent theory of Quantum Thermodynamics (QT) along the lines of classical thermodynamics lies in the fact that quantities such as work and heat cannot in general be described by Hermitian operators whose eigenvalues would give their expectation values. This has culminated into the "no-go" theorem that states that it is impossible to construct such (super)operators with proper physical properties [1]. The theorem can be circumvented by a Hamilton-Jacobi based approach to work, but in that case the total wave function of the system and the environment must be known [2]. In the simple limit of Markovian quantum evolution, work and heat can be identified from the change of the system Hamiltonian and its density matrix, respectively. This is based on the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) picture, where unitary and dissipative parts of open-quantum-system evolution can be separated. We have recently shown how any open-system evolution can be written in a generalized GKSL form, where this separation no longer holds [3].  By analysing trajectories given by the time evolution of the density matrix of the system we show how the internal energy change in the system can be unambiguously separated into entropy-generated and isentropic parts, identified as heat and work, respectively [4]. This allows consistent description of the First Law for any time-continuous evolution of an open quantum system.

1. M. Perarnau-Llobet, E. Bäumer, K. V. Hovhannisyan, M. Huber, and A. Acin, Phys. Rev. Lett. vol. 118, 070601 (2017).
2. R. Sampaio, S. Suomela, T. Ala-Nissila, J. Anders, and T.G. Philbin,  Phys. Rev. A vol. 97, 012131 (2018).
3. S. Alipour, A.T. Rezakhani, A.P. Babu, K. Mølmer, M. Möttönen, and T. Ala-Nissila, Phys. Rev. X vol. 10, 041024 (2020).
4. S. Alipour, A.T. Rezakhani, A. Chenu, A. del Campo, and T. Ala-Nissila, Phys. Rev. A Letters (2022).

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