Failure of the Jarzynski identity for a simple quantum system

Paul Bracken

Jing-ning Zhang, Kihwan Kim

Shuoming An, Jing-Ning Zhang, Mark Um +6 more

Shaul Mukamel

The distribution of work done on a quantum system by instantaneously changing the Hamiltonian is shown to satisfy the Jarzynski identity.

Chen Bai, Wenhao Li, Xian-Hui Ge

Abstract The Jarzynski identity can describe small-scale nonequilibrium systems through stochastic thermodynamics. The identity considers fluctuating trajectories in a phase space. The complexity geometry frames the discussions on quantum computational complexity using the method of Riemannian geometry, which builds a bridge between optimal quantum circuits and classical geodesics in the space of unitary operators. Complexity geometry enables the application of the methods of classical physics to deal with pure quantum problems. By combining the two frameworks, i.e., the Jarzynski identity and complexity geometry, we derived a complexity analog of the Jarzynski identity using the complexity geometry. We considered a set of geodesics in the space of unitary operators instead of the trajectories in a phase space. The obtained complexity version of the Jarzynski identity strengthened the evidence for the existence of a well-defined resource theory of uncomplexity and presented an extensive discussion on the second law of complexity. Furthermore, analogous to the thermodynamic fluctuation-dissipation theorem, we proposed a version of the fluctuation-dissipation theorem for the complexity. Although this study does not focus on holographic fluctuations, we found that the results are surprisingly suitable for capturing their information. The results obtained using nonequilibrium methods may contribute to understand the nature of the complexity and study the features of the holographic fluctuations.

Andreas Engel, Roman Nolte

The validity of the Jarzynski equation for a very simple, exactly solvable quantum system is analyzed. The implications of two different definitions of work proposed in the literature are investigated. The first one derives from measurements of the system energy at the beginning and at the end of the process under consideration making the work a classical stochastic variable with transition probabilities derived from quantum-mechanics. In the second definition an operator of work is introduced and the average in the Jarzynski equation is a quantum expectation value. For the first definition a general quantum-mechanical version of the Jarzynski equation is known to hold. For the second one the Jarzynski equation fails to yield the free energy difference at low temperature.