What is the difference between gibbs free energy and helmholtz free energy, and which is more applicable to biological systems?

The Gibbs free energy (G) of a system is a measure of the amount of usable energy (energy that a job can do) in that system. Changing Gibbs free energy during a reaction provides useful information about the energy and spontaneity of the reaction while Helmholtz free energy is a thermodynamic property that can be used to predict whether a process occurs spontaneously at constant volume and temperature.

Explanation:

Gibbs free energy is the most used for biological systems since it allows to relate the enthalpy change of the reactions occurred in the system and determine for example if they occur spontaneously or not, if they produce heat or absorb heat.

On the other hand, Helmholtz energy (also called Helmholtz function, Helmholtz free energy or work function) is an extensive quantity, thermodynamic potential and state function, of a thermodynamic system that measures the work obtainable in a closed system, in constant temperature conditions. . It does not depend on the process suffered, but on the final and initial state of the system

this would be a math