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Chemical engines can operate through various mechanisms, including utilizing chemical potential gradients to induce mechanical motion   [136, 137, 138], employing molecular motors that break chemical bonds   [139], as seen in adenosine triphosphate (ATP) hydrolysis   [140], and relying on Brownian motors driven by thermal diffusion, which can be described using Langevin and Fokker-Planck equations   [141]. Another approach involves leveraging surface energy from interfacial phenomena, such as the chemical Marangoni effect   [142]. In the quantum regime, engines that exchange both particles and energy with a thermal (thermochemical) reservoir, like the one explored in this work, are commonly referred to as quantum thermochemical engines   [4, 107, 113, 143].","type":"other"},{"key":"PhysRevE.111.054133Cc112R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.110.062612","type":"journal-article"},{"key":"PhysRevE.111.054133Cc113R1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/acc966","type":"journal-article"},{"key":"PhysRevE.111.054133Cc114R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1242308","type":"journal-article"},{"key":"PhysRevE.111.054133Cc115R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1803336115","type":"journal-article"},{"key":"PhysRevE.111.054133Cc116R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01343193","type":"journal-article"},{"key":"PhysRevE.111.054133Cc117R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.111.100502","type":"journal-article"},{"key":"PhysRevE.111.054133Cc118R1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/8\/5\/083","type":"journal-article"},{"key":"PhysRevE.111.054133Cc119R1","doi-asserted-by":"publisher","DOI":"10.1179\/174602206X90931","type":"journal-article"},{"key":"PhysRevE.111.054133Cc120R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.98.062132","type":"journal-article"},{"key":"PhysRevE.111.054133Cc121R1","unstructured":"The initial temperature of the working fluid, in thermal equilibrium with the cold reservoir, was kept constant at Tc=86.3nK, with an initial particle count Nc\u22432235 obtained using a chemical potential of \u03bc=7.95\u00d710\u221231J. In all cases, the interaction strength was quenched from gc=1.27\u00d710\u221238Jm to gh=1.8gc following Eq.   (5); during expansion, it was quenched back to gc per Eq.   (8). All results in this work pertain to a gas of Rb87 atoms with mass m\u22431.44\u00d710\u221225kg, three-dimensional scattering length as\u22435.31nm, trap frequency \u03c9\/2\u03c0=20.0Hz, and intial transverse confinement frequency \u03c9\u22a5\/2\u03c0=1.81kHz, achieving the interaction strength as gc\u22432\u210f\u03c9\u22a5a. In this and all subsequent figures, the timescale for the sudden quench is tw=0.05\/\u03c9, while for the quasistatic quench it is tw=300\/\u03c9.","type":"other"},{"key":"PhysRevE.111.054133Cc122R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.063636","type":"journal-article"},{"key":"PhysRevE.111.054133Cc123R1","doi-asserted-by":"publisher","DOI":"10.1088\/0031-8949\/91\/7\/075101","type":"journal-article"},{"key":"PhysRevE.111.054133Cc124R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.035301","type":"journal-article"},{"key":"PhysRevE.111.054133Cc125R1","doi-asserted-by":"publisher","DOI":"10.1126\/science.abf0147","type":"journal-article"},{"key":"PhysRevE.111.054133Cc126R1","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ac3659","type":"journal-article"},{"key":"PhysRevE.111.054133Cc127R1","unstructured":"R.\u00a0S. 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