Excess Entropy Production in Quantum System: Quantum Master Equation Approach

Abstract

For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by lnρ 0 and ρ 0 where ρ 0 is the instantaneous steady state of the QME andρ 0 is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime. *

Quantum Adiabatic Pumping in Rashba- Dresselhaus-Aharonov-Bohm Interferometer

“…wherer andt are given in Equations (27) and (25) and |σ is the spinor vector of spin σ. If we choose the AB phase φ and parameters of the interferometers, for example, X 0 or X 1 , but not the SOI strengths, we can show that the Berry curvature is finite in general as studied in Reference [26].…”

“…In addition to passive functional devices such as filters, the active functions, for example, spin-pumping or spin manipulation effect by dynamically modulating the gate voltages [7][8][9], magnetic field [10][11][12][13], or magnetization of the ferromagnets [14][15][16][17], has been investigated. In particular, quantum adiabatic pumping (QAP) phenomena [18,19], which stems from geometrical properties of the dynamics, is an active field of research [20][21][22][23][24][25]. In the non-interacting limit, QAP is related to the scattering matrix of the coherent transport.…”

Asymptotic expansion of the solution of the master equation and its application to the speed limit

“…Time-dependent open systems have been studied actively in recent years. These studies relate to quantum pump [1][2][3][4][5][6][7][8], excess entropy production [9][10][11][12][13], efficiency and power of heat engine [14][15][16][17][18], shortcuts to adiabaticity [19,20], and speed limits [21][22][23]. In the studies of quantum pumping and excess entropy production for systems governed by the master equation, the time dependence is described using the pseudo-inverse of the Liouvillian [1-3, 5-7, 12, 13, 24].…”

Alternative relativistic formulation of linear spectrum of hydrogen-like systems

“…At present, it is considered that the most effective way to describe the electronic properties of a matherial is a discrete-stochastic modelling of the spectral picture of the energy characteristics of the matherial's particles, implemented using methods of modern quantum mechanical calculations [Miao et al, 2014;Sych and Leuchs, 2015;Ogata, 2016;Nakajima and Tokura, 2017;Han, Xu and Qin, 2018]. Along with this, there is another opinion openly expressed by many well-known scientists, for example, Professor N. Kobayashi of the University of Tokyo: "This task is extremely difficult, because the existing methods of modeling atomic and molecular structures are imperfect and require too much time.…”