Helmholtz free energy is a thermodynamic potential that measures the useful work obtainable from a closed system at constant temperature and volume. It is denoted by the symbol A or F and is defined as the internal energy of the system minus the product of its temperature and entropy. This concept helps predict the direction of spontaneous processes and the equilibrium state of a system. In practical terms, Helmholtz free energy is important in fields like physical chemistry and statistical mechanics. It provides insights into the stability of systems and is used to analyze reactions and phase transitions, helping scientists understand how energy is distributed in various states of matter.