Quantum Thermodynamics: A Nonequilibrium Green’s Function Approach

Abstract

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit. DOI: 10.1103/PhysRevLett.114.080602 PACS numbers: 05.70.Ln, 05.60.Gg Nonequilibrium thermodynamics of open quantum systems is a powerful tool for the study of mesoscopic and nanoscale systems. It allows one to reliably assess the performance of energy-converting devices such as thermoelectrics or photoelectrics, by identifying the system entropy production. It enables one to meaningfully compare these different devices by discriminating the systemspecific features from the universal ones and to appraise the role of quantum effects. It can also be used to verify the thermodynamic consistency of approximation schemes. Such a theory is nowadays available for systems weakly interacting with their surrounding [1][2][3][4][5][6], where it has proven very useful [7][8][9][10][11][12][13][14][15]. However, in case of strong system-reservoir interactions, finding definitions for heat, work, entropy, and entropy production, which satisfy the basic laws of thermodynamics is an open problem. Each proposal has its own limitations [16][17][18][19][20][21][22][23], even at equilibrium [24][25][26][27][28][29][30]. Reversible transformations, for instance, are never explicitly characterized. Establishing a consistent nonequilibrium thermodynamics for open quantum systems strongly coupled to their surrounding is therefore an important step towards a more realistic thermodynamic description of mesoscopic and nanoscale devices. It is also essential to improve our understanding of the microscopic foundations of thermodynamics.In this Letter, we use the nonequilibrium Green's functions (NEGF) to establish a fully consistent nonequilibrium thermodynamic description of a fermionic single quantum level strongly coupled to multiple fermionic reservoirs. A slow time-dependent driving force controls the level energy as well as the system-reservoir interaction. We propose definitions for the particle number, the energy, and the entropy of the system, as well as for entropy production, heat, and work, which give rise to a consistent zeroth, first, second, and third law. These definitions can be seen as energy resolved versions of the weak coupling definitions used in stochastic thermodynamics. An interesting outcome of our approach is that the general form of the energy and particle currents is different from the standard form used in the NEGF and cannot be expressed as an expectation value of operators. We recover the known expressions when considering nonequilibrium steady states (i.e., in absenc...

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

“…We provide in Section 3.2 some numerical calculations of the entropy production rate for a model system of a single electron resonance coupled to two Fermi reservoirs. A comparison to earlier results [11] is also given. In Section 4, we consider the NE entropy production in the entire system obtained from the Gibbs-von Neumann expression based on the NE density matrix.…”

“…One can study the NE thermodynamical properties and the entropy production in such systems when an external driving force is applied to the central region. The time dependence of the external force can be arbitrary or periodic [10,11,13,15]. The long-time limit behaviour of the NE thermodynamics also presents very interesting properties [12][13][14].…”

“…Originally the weak coupling limit of a finite-size central region interacting with thermal and/or particle baths was first considered [1, 2,[4][5][6]. Methods for dealing with the strong coupling limit have been recently developed [7][8][9][10][11][12][13][14]. One can study the NE thermodynamical properties and the entropy production in such systems when an external driving force is applied to the central region.…”

Charge Transport and Entropy Production Rate in Magnetically Active Molecular Dimer

“…From the same standpoint, thermal transport studies were conceived and came to be conclusive in the upcoming years [2]. Subsequently, several theoretical studies demonstrated the possibility to conduct both thermal and charge through tunneling junctions [26][27][28][29][30][31][32][33][34], both in presence and absence of lattice vibrations, although there is no generic framework that successfully is capable of describing the thermodynamic properties of nano junctions [8,14,35].…”

“…Several realizations of tunneling junctions comprising noble metal electrodes and polymers that absorb, emit, and transmit thermal have been reported [4,6]. The interest is, moreover, driven from the perspective of information science and technology with respect to entropy production rate [3,7] and the meaning of the thermodynamics in low dimensional systems [3,8,9]. This was motivated by the discovery of conducting polymers and solitonic electronic transport mechanisms discovered by Shirakawa, see [10] and references therein.…”