Work harvesting by q-deformed statistical mutations in an Otto engine

We consider a semi-classical heat engine with a $q$-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter $q$ on the work and efficiency of the engine. In usual heat engines, a Hamiltonian parameter is varied during the work injection and extraction stages while the quantum statistical character of the working substance remains fixed. We point out that even if the Hamiltonian parameters are not changing, work can be harvested by quantum statistical changes of the working substance. Work extraction from thermal resources using quantum statistical mutations of the working substance makes a semi-classical engine cycle without any classical analog. As a concrete example of such a semi-classical heat engine with a profound quantum character, we consider the Otto cycle and use the deformation parameter to define the isentropic steps while keeping the Hamiltonian parameters constant. We verify that our conclusion applies to both bosonic and fermionic oscillator deformations.