Thermodynamics is one of the most successful physical theories, and its basic laws are believed to govern universally the behavior of systems consisting of a macroscopic number of particles. The second law of thermodynamics, for instance, which states that the entropy in an isolated system does not decrease, has been verified in experiments spanning vastly different length scales and is at the origin of many phenomena of our everyday lives.
For classical systems, statistical physics provides a microscopic justification of the laws of thermodynamics. For quantum systems, these laws can be derived using techniques such as the Born-Markov approximation, which are valid for weak coupling. However, it has emerged over the past years that it is not straightforward to find consistent definitions of thermodynamic quantities, such as heat and entropy, in driven quantum systems which are strongly coupled to reservoirs. Such strong coupling can easily be realized, for instance, in quantum dots coupled to fermionic reservoirs.
In order to shed light on this question, we have investigated the simplest prototypical model, namely a noninteracting resonant level model coupled to fermionic reservoirs. Using an exact solution of the fully driven quantum mechanical model, we show how to define observable thermodynamical quantities which allow the derivation of a first and second law of thermodynamics.