01618nas a2200157   4500000000100000000000100001008004100002260001000043100003200053700002200085700001900107245002100126856004700147490000600194520126000200       2024                            d  c07/241 aHanna Wojewódka-Ściążko1 aZbigniew Puchała1 aKamil Korzekwa00aResource engines  uhttps://doi.org/10.22331/q-2024-01-10-12220 v83 a<p>In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two--stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.</p>