The entropy production rate of double quantum-dot system with Coulomb coupling

Abstract

In thermodynamics of irreversible processes, the entropy production rate (EPR) is usually generated by the rate of the entropy change of the system due to its internal transitions and the entropy flows due to the interactions between the system and the environment. For the bipartite system, in addition to the factors mentioned above, the energy and information exchanges between the two subsystems will generate an additional entropy production in the EPR of a subsystem. To reveal the essence and role of the information flow, we build an open dissipative quantum system coupled to multiple electronic reservoirs with the same temperature and different chemical potentials. Based on the thermal and electron transport properties of a double quantum-dot system with Coulomb coupling, the EPR of each quantum dot and the information flow between subsystems are studied. Starting from the quantum master equation under the Born, Markov, and rotating-wave (or secular) approximations, we derive the EPRs of the total system and subsystems at the steady state. For purposes of relating the thermodynamic properties to the fundamental fluxes and affinities, a graph representation of the dynamics of the four-state model is introduced. Selecting a directed graph and a complete set of basic cycles by using Schnakenberg’s network theory, we show how the EPRs of the total system and the subsystems relate to global and local cycle fluxes. It is found that the energy and information exchanges between the quantum dots depend on the global cycle flux. The EPRs induced by the electron flows due to the chemical potential difference as well as the energy and information exchanges between the subsystems are the key elements of thermodynamic irreversibilities. The EPRs caused by the information exchange guarantee the continuous electron transports. The EPRs and the coarse-grained EPRs of the subsystems varying with the Coulomb coupling strength are obtained numerically. The results demonstrate that the information flows in the process of internal exchange become important to fully understand the operation mechanism of the bipartite system. Without violating the second law of thermodynamics, the information can be regarded as a driving force to move electrons from low to high chemical potential.