Maximizing Entropy vs Minimizing Gibbs Function - Why?

In summary: When you maximize entropy, you're maximizing the disorder of the system. When you minimize entropy, you're minimizing the disorder of the system. However, as long as the other constraints are held constant, the two methods will always give the same result.
  • #1
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It occurs to me that some people create codes to maximize the entropy of a system in order to predict equilibrium concentrations. However, others minimize the Gibbs function. I understand the relationship, so why the two methods? Aren't these results always the same? Is there a practical reason for this?
 
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  • #2
There is a difference in what these energy apply to.

Basically maximizing the total entropy of system+reservoir is (under special circumstances only!) equivalent to minimizing the Gibbs energy of the system alone.

It is incorrect to minimize the entropy of the system alone. Also the contraints (pressure or temperature kept constant?) matter for the decision whether to use Gibbs energy or one of the other three potentials (Helmholtz, Energy, Enthalpy).
 
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  • #3
Gerenuk said:
There is a difference in what these energy apply to.

Basically minimizing the total entropy of system+reservoir is (under special circumstances only!) equivalent to minimizing the Gibbs energy of the system alone.

It is incorrect to minimize the entropy of the system alone. Also the contraints (pressure or temperature kept constant?) matter for the decision whether to use Gibbs energy or one of the other three potentials (Helmholtz, Energy, Enthalpy).

Surely you mean maximize entropy?

We start with the differential expression for energy, [itex]dU=T\,dS-P\,dV+\sum_i \mu_i\,dN_i+\dots[/itex]. For systems at constant entropy, volume, and mass (and all other extensive variables constant), we minimize the potential U (the internal energy).

We can rewrite the equation as [itex]-dS=-1/T\,dU-P/T\,dV+\sum_i \mu_i/T\,dN_i+\dots[/itex]. So for systems at constant energy, volume, and mass, we maximize the potential S (the entropy).

We can always derive various different potentials for variations on the system. If the entropy, pressure, and mass are constant, for example, we use the Legendre transform [itex]H=U+PV[/itex] to get [itex]dH=-T\,dS-V\,dP+\sum_i \mu_i\,dN_i[/itex]. Thus, we minimize the enthalpy H for these systems.

If the temperature, pressure, and mass are constant (a frequent scenario), we minimize the Gibbs potential [itex]G=U+PV-TS[/itex]. If the temperature, volume, and chemical potential of species i are constant, we minimize the potential [itex]\Lambda=U-TS-\mu_i N_i[/itex]. And so on.

Callen's Thermodynamics has a nice discussion of this. It all comes from the tendency for total entropy to be maximized (i.e., Second Law).
 

1. What is the difference between maximizing entropy and minimizing Gibbs function?

Maximizing entropy and minimizing Gibbs function are two different approaches to understanding thermodynamic systems. Entropy is a measure of the disorder or randomness of a system, while Gibbs function is a measure of the energy available to do work. Maximizing entropy means increasing the disorder of a system, while minimizing Gibbs function means decreasing the energy available to do work.

2. Why do we need to maximize entropy or minimize Gibbs function?

In thermodynamics, there is a fundamental principle known as the second law of thermodynamics, which states that the total entropy of a closed system will always increase over time. This means that in order for a system to be in equilibrium, the entropy must be maximized or the Gibbs function must be minimized. This is necessary for a system to reach a state of maximum stability.

3. Can both entropy and Gibbs function be maximized or minimized simultaneously?

No, entropy and Gibbs function are inversely related. This means that when one is maximized, the other is minimized. Therefore, it is not possible for both to be maximized or minimized at the same time.

4. How do maximizing entropy and minimizing Gibbs function affect the behavior of a system?

Maximizing entropy leads to an increase in disorder and randomness in a system, making it less organized. On the other hand, minimizing Gibbs function decreases the energy available to do work, which can result in a system becoming more stable. Both of these principles help to maintain equilibrium in a system.

5. Can the concepts of entropy and Gibbs function be applied outside of thermodynamics?

While entropy and Gibbs function are fundamental concepts in thermodynamics, they can also be applied to other fields such as information theory and economics. In information theory, entropy is used to measure the uncertainty or randomness of a system, while Gibbs function can be used to analyze economic systems and decision-making processes.

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