Free Energy
Free Energy is a
thermodynamic potential defined in terms of classic thermodynamic variables temperature, pressure, density, internal energy, and entropy, by
Herman von Helmholtz and
J. Willard Gibbs.
The
Free Energy Principle is a mathematical concept defined by
Karl Friston. It has nothing to do with thermodynamics.
Helmholtz Free Energy
The Helmholtz free energy is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.
The Helmholtz free energy is defined as
A ≡ U - TS,
where
-
U is the internal energy of the system (SI: joules, CGS: ergs),
-
T is the absolute temperature (kelvins) of the surroundings, modelled as a heat bath,
-
S is the entropy of the system (SI: joules per kelvin, CGS: ergs per kelvin).
Gibbs Free Energy
The Gibbs energy is the
thermodynamic potential that is minimized when a system reaches chemical equilibrium at constant temperature (isothermal) and pressure (isobaric).
In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.
The Gibbs free energy is defined as
G(p,T) ≡ U + pV - TS = H + pV}
where
-
p is the pressure of the system),
-
V is the volume of the system,
-
H is the Helmholtz free energy.
Friston Free Energy Principle
The free energy principle is a mathematical principle of information physics. Its application to fMRI brain imaging data as a theoretical framework suggests that the brain reduces surprise or uncertainty by making predictions based on internal models and uses sensory input to update its models so as to improve the accuracy of its predictions
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