Thermodynamic Equilibrium and Free Energy

Table of Contents

To understand how organisms live on free energy, it helps to look at a few basic ideas from thermodynamics and see how they apply to cells.

Thermodynamic Equilibrium

In thermodynamics, a system is in equilibrium when:

All macroscopic (large-scale) properties are constant in time.
There are no net flows of matter or energy within the system or between the system and its surroundings.
No further spontaneous changes occur unless the system is disturbed from the outside.

In such a state, the system is “done” changing; it has reached a balance. For many simple physical systems, equilibrium is the final state that is reached spontaneously—for example, when a drop of dye diffuses evenly through a glass of water.

For living cells, true thermodynamic equilibrium would mean:

No net chemical reactions proceeding in a particular direction.
No gradients of ions, molecules, or temperature.
No directed flows of energy.

A system at equilibrium cannot perform work. Therefore, a cell at true thermodynamic equilibrium is dead. Life is only possible as long as the cell is away from equilibrium and maintains this imbalance over time.

Biological systems instead operate in a steady state (treated in the next subsection), in which flows and reactions continue but are balanced overall. The important point here is:

Spontaneous processes tend to move toward equilibrium.
Living systems continuously counteract this tendency by using energy.

This is where free energy comes into play.

Free Energy: Concept and Sign

In biology, we usually use the Gibbs free energy $G$ to describe energy changes in reactions under constant temperature and pressure (conditions typical of cells).

The change in Gibbs free energy in a process is written as $\Delta G$.

$\Delta G < 0$: the process is exergonic (releases free energy) and can occur spontaneously (without external energy input).
$\Delta G > 0$: the process is endergonic (requires an input of free energy) and is non-spontaneous in the given direction.
$\Delta G = 0$: the system is at equilibrium. There is no net change; the forward and reverse reactions occur at the same rate.

Free energy is called “free” because it is the portion of a system’s energy that is available to do work—such as:

Mechanical work (muscle contraction).
Transport work (pumping ions across a membrane).
Chemical work (synthesizing complex molecules).

A biological process can proceed spontaneously only if the overall $\Delta G$ is negative. This does not mean that endergonic steps cannot occur; it means that, taken together, all coupled steps must have a negative total $\Delta G$.

Equilibrium Constant and Free Energy

For a simple chemical reaction:
$$
\text{A} + \text{B} \rightleftharpoons \text{C} + \text{D}
$$

we can define an equilibrium constant $K$ (under given conditions) as:
$$
K = \frac{[\text{C}][\text{D}]}{[\text{A}][\text{B}]}
$$
where the brackets denote concentrations at equilibrium.

Thermodynamics links $K$ to the standard free energy change $\Delta G^\circ$ of the reaction:
$$
\Delta G^\circ = -RT \ln K
$$
where:

$R$ is the gas constant,
$T$ is the absolute temperature (in kelvin),
$\ln$ is the natural logarithm.

Interpretation:

If $K > 1$, then $\ln K > 0$, so $\Delta G^\circ < 0$: at equilibrium, products are favored, and under standard conditions the reaction tends to go in the forward direction.
If $K < 1$, then $\ln K < 0$, so $\Delta G^\circ > 0$: reactants are favored, and under standard conditions the forward reaction is not spontaneous.

However, inside a cell, actual concentrations often differ from standard conditions. The actual free energy change $\Delta G$ is related to $\Delta G^\circ$ and the current concentrations by:
$$
\Delta G = \Delta G^\circ + RT \ln Q
$$
where $Q$ is the reaction quotient:
$$
Q = \frac{[\text{C}][\text{D}]}{[\text{A}][\text{B}]}
$$

When $Q = K$, then $\Delta G = 0$ and the system is at equilibrium.
When $Q < K$, then $\ln Q < \ln K$, and $\Delta G$ will be negative; the reaction tends to move forward (toward more products).
When $Q > K$, the reaction tends to move backward (toward more reactants).

Cells exploit this dependence on concentrations to keep many reactions operating far from equilibrium.

Direction of Reactions and Equilibrium in Cells

While each individual chemical reaction has an equilibrium point, living cells:

Keep many reactions far from their equilibrium concentrations.
Use continuous fluxes of substrates and removal of products to pull reactions in a desired direction.
Use enzyme-catalyzed pathways where some steps are strongly exergonic and effectively irreversible under cellular conditions.

The relation between $\Delta G$ and equilibrium explains:

Why an exergonic reaction can “drive” an endergonic one if they are coupled.
Why metabolic pathways can proceed in one direction overall, even though individual reactions are reversible.

When a reaction is very close to equilibrium in a cell (i.e., $\Delta G \approx 0$):

A small change in concentrations can reverse its direction.
Such reactions often serve as regulators or “valves” in metabolism, easily adjusting flux depending on cellular needs.

Strongly negative-$\Delta G$ steps, in contrast, are usually key control points and help set the direction of the pathway.

Free Energy and ATP Coupling (Conceptual Link)

Details of ATP are treated in a later chapter, but in thermodynamic terms:

Hydrolysis of ATP to ADP and inorganic phosphate ($\text{Pi}$) has a strongly negative $\Delta G$ under cellular conditions.
Cells couple ATP hydrolysis to many endergonic reactions, forming an overall reaction with $\Delta G_{\text{total}} < 0$.

Symbolically:
$$
\Delta G_{\text{endergonic}} > 0,\quad
\Delta G_{\text{ATP hydrolysis}} \ll 0
$$
$$
\Delta G_{\text{total}} = \Delta G_{\text{endergonic}} + \Delta G_{\text{ATP hydrolysis}} < 0
$$

This thermodynamic principle allows the cell to carry out processes that would not proceed spontaneously on their own, while still respecting the rule that the overall process moves in the direction of decreasing free energy.

Why Life Requires Being Away From Equilibrium

From a thermodynamic perspective, the essential features are:

Spontaneous processes decrease free energy and drive systems toward equilibrium.
A system at equilibrium can no longer perform work.
Living cells maintain:

Concentration gradients (e.g., ions across membranes),
Chemical nonequilibrium (e.g., high ATP/ADP ratio),
Organized structures (e.g., macromolecules, membranes),

all of which correspond to states of higher free energy than the surroundings.

To sustain these nonequilibrium states, organisms:

Import high-free-energy substances or energy (light, chemical energy).
Convert this input into useful work and heat.
Export low-free-energy products and waste.

Thus, “living on free energy” means continuously using free energy to oppose the natural drift toward thermodynamic equilibrium, while always obeying the basic laws that: