AQP Seminar: Time-dependent temperature and entropy production rate of a single-mode Gaussian state under Markovian and non-Markovian dynamics.

Aalto Quantum Physics Seminar (Nanotalo). Speaker: Takaaki Aoki (AIST, The University of Tokyo)

In recent years, due to the development of nanotechnology, research on quantum thermodynamics [1] has become more and more active. In particular, how to define thermodynamical quantities like heat, work, and temperature in microscopic quantum systems is a fundamental and important problem. Here, we consider one quantum harmonic oscillator attached to many quantum harmonic oscillators. We restrict the quantum state of the total system to a Gaussian state [2,3], which makes the quantum states of the subsystems Gaussian states, too. By doing so, we can easily calculate various physical quantities analytically. We calculate the time derivative of the von Neumann entropy of one harmonic oscillator under Markovian and non-Markovian dynamics. Then, we decompose this into the entropy flux rate and the entropy production rate. Moreover, we define the time-dependent temperature of one harmonic oscillator from the relation between the entropy flux rate and the heat flux rate. In Markovian case, the entropy production rate is always non-negative, which satisfies the second law of thermodynamics. However, in non-Markovian case, the entropy production rate can be negative, which may show the violation of the second law.

[1] S. Vinjanampathy and J. Anders, Contemp. Phys. 57, 545 (2016).
[2] A. Serafini, Quantum Continuous Variables: A Primer of Theoretical Methods (CRC
Press, Taylor & Francis Group, Boca Raton, FL, 2017).
[3] C. Weedbrook, S. Pirandola, R. Garc ́ıa-Patr ́on, N.J. Cerf, T.C. Ralph, J.H. Shapiro, and
  S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).