= Solution
A useful organizing principle is <Gibbs free energy>: at specified <temperature> and <pressure> a coupled process is favorable when its total $\Delta G$ is negative. For each <chemical species>,
$$
\mu_i=\mu_i^\circ+RT\ln a_i,\qquad
\Delta G=\Delta G^\circ+RT\ln Q.
$$
The relative amounts of <chemical substances> determine the available <Gibbs free energy>, beyond counting <energy> in individual bonds. Nutrient oxidation and light-driven chemistry can maintain nonequilibrium compositions. <ATP hydrolysis> can drive biosynthesis, transport and motion of <molecular motors> when reactions are coupled so that their total free-energy change is favorable. Breaking an <inorganic phosphate> bond itself costs <energy>; the favorable net <hydrolysis> includes formation and solvation of the products and depends on their <thermodynamic activities>.
<Redox> <Gibbs free energy> comes from transferring electrons between donors and acceptors: $\Delta G=-nF\Delta E$. Electron transfer in respiration or photosynthesis can help establish an <electrochemical gradient>. For a mole of <ions> moving from side 1 to side 2,
$$
\Delta\widetilde\mu=RT\ln(a_2/a_1)+zF(\psi_2-\psi_1).
$$
The <concentration> and electrical terms together drive transport and can power <ATP synthase>. ATP-driven pumps can conversely build gradients. <Chemiosmosis> is the coupling between this gradient and chemical synthesis, not the creation of <Gibbs free energy> by an <enzyme>.
Mechanical <work> and elastic storage are other forms: a motor can do $\int F\,dx$ or $\int\tau\,d\theta$, and an approximately Hookean element stores $kx^2/2$. ATP-driven motors convert <Gibbs free energy> into motion, while externally forced reverse motion can sometimes drive chemical synthesis. A <photon> brings <energy> $h\nu$; light <photon absorption> initiates chemistry in photosynthesis and light-driven pumps, with some <energy> inevitably dissipated. Living cells use these conversions for structure, movement, homeostasis and synthesis, while releasing <heat> and exporting <entropy>. At a single uniform <temperature>, dissipated <heat> cannot be completely recycled into useful work.
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