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photosynthesis to energy storage systems such as fuels and batteries. Here, we consider the maximization of free energy\u2014and by extension, the maximum extractable work\u2014that can be gained by a classical or quantum system that undergoes driving by its environment. We consider how the free energy gain depends on the initial state of the system while also accounting for the cost of preparing the system. We provide simple necessary and sufficient conditions for increasing the gain of free energy by varying the initial state. We also derive simple formulae that relate the free energy gained using the optimal initial state rather than another suboptimal initial state. Finally, we demonstrate that the problem of finding the optimal initial state may have two distinct regimes, one easy and one difficult, depending on the temperatures used for preparation and work extraction. We illustrate our results on a simple model of an information engine.<\/jats:p>","DOI":"10.3390\/e27010091","type":"journal-article","created":{"date-parts":[[2025,1,21]],"date-time":"2025-01-21T08:46:26Z","timestamp":1737449186000},"page":"91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Maximizing Free Energy Gain"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3518-9208","authenticated-orcid":false,"given":"Artemy","family":"Kolchinsky","sequence":"first","affiliation":[{"name":"Department of Medicine and Life Sciences, Universitat Pompeu Fabra, 08003 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iman","family":"Marvian","sequence":"additional","affiliation":[{"name":"Physics and Electrical Engineering, Duke University, Durham, NC 27708, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Can","family":"Gokler","sequence":"additional","affiliation":[{"name":"School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3402-9763","authenticated-orcid":false,"given":"Zi-Wen","family":"Liu","sequence":"additional","affiliation":[{"name":"Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Shor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Center for Theoretical Physics and CSAIL, MIT, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oles","family":"Shtanko","sequence":"additional","affiliation":[{"name":"IBM Quantum Almaden, San Jose, CA 95120, USA"},{"name":"Department of Physics, MIT, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kevin","family":"Thompson","sequence":"additional","affiliation":[{"name":"Sandia National Laboratory, Albuquerque, NM 87123, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3105-2869","authenticated-orcid":false,"given":"David","family":"Wolpert","sequence":"additional","affiliation":[{"name":"Santa Fe Institute, Santa Fe, NM 87501, USA"},{"name":"Center for Bio-Social Complex Systems, Arizona State University, Tempe, AZ 85287, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seth","family":"Lloyd","sequence":"additional","affiliation":[{"name":"Department of Physics, MIT, Cambridge, MA 02139, USA"},{"name":"Department of Mechanical Engineering, MIT, Cambridge, MA 02139, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1103\/PhysRevLett.78.2690","article-title":"Nonequilibrium equality for free energy differences","volume":"78","author":"Jarzynski","year":"1997","journal-title":"Phys. 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