Gibbs energy, represented as G = H - TS, is the total energy available in a system at constant temperature and pressure, making it crucial for analyzing isothermal and isobaric processes. The change in Gibbs free energy (ΔG = ΔH - TΔS) determines whether a process is spontaneous, depending on the sign of ΔG. It is particularly significant in open systems or chemical reactions where particle numbers vary. The relationship between Gibbs energy and chemical potentials is expressed as G = Σ Ni μi, highlighting the extensive nature of particle numbers. Understanding Gibbs energy is essential for evaluating the feasibility of thermodynamic processes.