Carnot Efficiency and Zero-Entropy Production Rate Do Not Guarantee Reversibility of a Process

A thermodynamic process at a zero-entropy production (EP) rate has been regarded as a reversible process. A process achieving the Carnot efficiency is also considered a reversible process. Therefore, the condition, ‘Carnot efficiency at zero-EP rate’ can be regarded as a strong condition for a reversible process. Here, however, we show that the detailed balance can be broken for a zero-EP rate process and even for a process achieving the Carnot efficiency at a zero-EP rate in an example of a quantum-dot model. This clearly demonstrates that ‘Carnot efficiency at zero-EP rate’ or just ‘zero-EP rate’ is not a sufficient condition for a reversible process.