Distinguishability as a Resource – Thermodynamic Characterization of 1D Anyons

In low-dimensional systems, indistinguishable particles can display statistics that interpolate between those of bosons and fermions. Signatures of these “anyons” have been detected in two-dimensional quasiparticle excitations of the fractional quantum Hall effect, however experimental access to these quasiparticles remains limited. In one dimension, anyonic behavior can be realized through a statistical mixture of entangled particles. Here we develop the full thermodynamic characterizations of one-dimensional anyons, including both equilibrium and nonequilibrium behavior. The performance of a quantum heat engine with an anyonic working medium is explored, demonstrating a rich dependence on the anyonic phase. In addition, methods of optimizing engine performance through shortcuts to adiabaticity are investigated, using both linear response and fast forward techniques.