We study the heat generation in a nanodevice with an electric current passing through the device. A general formula for the heat generation is derived by using the nonequilibrium Keldysh Green’s functions. This formula can be applied in both the linear and nonlinear transport regions, for time-dependent systems, and with multiterminal devices. The formula is also valid when the nanodevice contains various interactions. As an application of the formula, the heat generation of a lead–quantum-dot–lead system is investigated. The dc and ac biases are studied in detail. We find several interesting behaviors, e.g., the heat generation $Q\ne IV$ (with the current $I$ and bias $V$), that are unique to nanostructures, revealing significant difference from heat generation in macroscopic systems.

• Received 28 December 2006

DOI:https://doi.org/10.1103/PhysRevB.75.155306