  We build a double quantum-dot system with Coulomb coupling and aim at
studying the connections among the entropy production, free energy, and
information flow. By utilizing the concepts in stochastic thermodynamics and
graph theory analysis, the Clausius and nonequilibrium free energy inequalities
are built to interpret the local second law of thermodynamics for subsystems. A
fundamental set of cycle fluxes and affinities is identified to decompose the
two inequalities by using Schnakenberg's network theory. The results show that
the thermodynamic irreversibility has the energy-related and
information-related contributions. A global cycle associated with the
feedback-induced information flow would pump electrons against the bias
voltage, which implements a Maxwell Demon.
