We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing in mind. Additional relations are given, which relate the exponentiated work in quantum and simulated (classical) annealing. It is also suggested that the Jarzynski equality may serve as a guide to develop a method to perform quantum annealing under non-adiabatic conditions.

Real time nanoscale structural evaluation of gold structures on Si (100) surface using in-situ transmission electron microscopyThe authors propose a simple new method for fabricating stable nanotips using sharpened Au-Mo alloy tips. By annealing at 1000-1200 K in UHV, Au atoms segregate to the alloy surface to form a Au film of one physical monolayer thickness, resulting in formation of nanopyramids on the ͑111͒ surface. Although field ion microscopy images of the nanotips show no single-atom termination similar to the previous cases of Au-deposited W nanotips, energy spectra of the emitted electrons strongly suggest the realization of a single-atom termination just after annealing.

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The Jarzynski equality (JE) is known as an exact identity for nonequillibrium systems [1]. The JE was originally formulated for isolated and isothermal systems, while Adib reported an JE extended to an isoenergetic process [2]. On an isoenergetic process, the functional form of the Hamiltonian is altered with the energy fixed at a constant value E under the effect of an aritificial field term which is added to the Hamilton dynamics. This kind of JE is useful to calculate the entropy which replaces the Helmholtz free energy appearing in the original JE.On the other hand, the limitation of the constant energy seems to be an obstacle to widely apply the JE to more interdisciplinary problems such as optimization problems. Another problem is that it takes too long time to estimate some physical quantities since the entropy at the different energy values cannot be calculated at the same time with the JE. In the present paper, we extend the JE to an energy-controlled system in order to overcome these difficulties. In our study, we make it possible to control the instantaneous value of the energy arbitrarily in a nonequilibrium process. Under our extension, the new JE is more practical and useful to calculate the number of states and the entropy than the isoenergetic one. Furthermore, we expect that our JE can be used also for applications to computation and information science beyond physics. We will show an instance of possible application of our JE to a kind of optimization problems which is equivalent to physical problems to find the ground state [3].

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