QUROPE Quantum Information Processing and Communication in Europe

Fundamental limitations for quantum and nanoscale thermodynamics
M. Horodecki and J. Oppenheim
Nature Communications 4, 2059 (2013) and

Truly work-like work extraction via a single-shot analysis
J. Aberg
Nature Communications 4, 1925 (2013)

The relationship between thermodynamics and statistical physics is valid in the thermodynamic limit, when
the number of particles becomes very large, and fluctuations become negligible. However, one can study
thermodynamics in the opposite regime, for small systems, when quantum effects become important and
fluctuations relevant.

In their work Horodecki and Oppenheim and independently Aberg studied aspects of thermodynamics in this
regime. The free energy, a central concept to thermodynamics, governs both the maximal amount of work
one can extract from a system in contact with a thermal bath and the minimal cost one has to pay to
reproduce such a state starting at equilibrium. These coincide since thermodynamics is a reversible theory. In
these works it is shown that in the quantum regime that the amount one can extract almost deterministically
(i.e. will almost no fluctuations) and the amount one has to pay in fact differ, and that each is bounded by a
different free energy like quantity. Thus fluctuations and quantum coherence stop the theory from being
reversible, which is only recovered in the usual thermodynamic limit.