# Carnot efficiency and zero-entropy-production rate do not guarantee reversibility of a process

## TL;DR

This paper demonstrates through a quantum-dot model that achieving Carnot efficiency at zero entropy production rate does not necessarily imply a reversible thermodynamic process, challenging common assumptions.

## Contribution

It provides a counterexample showing that zero entropy production and Carnot efficiency are not sufficient for reversibility in thermodynamic processes.

## Key findings

- Zero-EP rate process can break detailed balance.
- Carnot efficiency at zero-EP rate does not guarantee reversibility.
- Quantum-dot model illustrates the non-equivalence.

## Abstract

Thermodynamic process at zero-entropy-production (EP) rate has been regarded as a reversible process. A process achieving the Carnot efficiency is also considered as a reversible process. Therefore, the condition, `Carnot efficiency at zero-EP rate' could be regarded as a strong equivalent 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 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.