Abstract:

The consistency of a thermodynamic model is its capability of giving predictions that are in agreement with the first and second laws of thermodynamics. A possible way to obtain a thermodynamically consistent description of an open quantum system is to consider the degrees of freedom of the environment explicitly, and introduce the relevant thermodynamic quantities (such as heat, work and entropy) at the level of the global picture including both system and environment [1].
However, the full dynamics of the environment is often very difficult to solve, and its knowledge is redundant if we are interested in only a few key properties of the system energetics. For this reason, it is often preferable to work at the level of the reduced system dynamics, after performing some approximations. In this talk we will discuss how different approximation schemes preserve the validity of the laws of thermodynamics, with a particular attention to the preservation of fluctuation theorems (FTs) [1,2].  

In the first part, we focus on quantum master equations (QMEs) and derive a general condition for a time-local QME to satisfy the first and second laws of thermodynamics at the fluctuating level. In this context, we show that the fluctuating second law can be rephrased as a Generalized Quantum Detailed Balance condition (GQDB) i.e. a symmetry of the time-local generators which ensures the validity of the FT [3]. The connection between this new condition and the usual notion of detailed balance, that holds for secular master equations, is discussed in detail. We finally test the GQDB for the Redfield equation and for another beyond secular QME recently introduced in the literature [4].
In the second part of the talk, we look for a more general approach to encompass the thermodynamics of quantum systems far away from the weak coupling and markovian regimes. To do so, we will use a generalization of the Keldysh contour, and prove that the FT can be expressed as a symmetry of such a contour [5]. We will discuss in detail the Keldysh idea [6], and explain how its extension can be useful for the calculation of energy statistics in closed and open quantum systems.

[1] M. Esposito, U. Harbola and S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009) 

[2] M. Campisi, P. Hanggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011) 

[3] A. Soret, V. Cavina and M. Esposito, Physical Review A 106, 062209 (2022)

[4] G. McCauley, et al. npj Quantum Information 6, 1 (2020) 

[5] V. Cavina, et al. arXiv preprint arXiv:2304.03681 (2023) 

[6] L. V. Keldysh, Sov. Phys. JETP 20.4 1018 (1965) 

Bio:

I am currently a postdoctoral researcher in the group of Prof. Massimiliano Esposito at the University of Luxembourg, where my research is mainly focused on quantum thermodynamics, stochastic thermodynamics and open quantum systems. These were also the main research topics of my Phd, that I obtained in 2019 under the supervision of Prof. Vittorio Giovannetti in Scuola Normale Superiore of Pisa, with a project centered on the optimization of quantum engines by using optimal control theory.
Over the years I explored several fields related to the theory of open quantum systems, such as quantum metrology, quantum optics, and critical phenomena.