Energy conservation alone does not determine which thermodynamic processes occur spontaneously. The second law of thermodynamics introduces a state quantity called entropy that constrains the direction of real processes.

For a reversible transfer of heat $\delta Q_{rev}$ at absolute temperature $T$,

$$dS=\frac{\delta Q_{rev}}{T}.$$

Isolated systems

For an isolated system,

$$\Delta S\ge0.$$

Entropy remains constant for an ideal reversible process and increases for an irreversible one.

Irreversibility

Heat spontaneously flowing from hot to cold, friction, diffusion and mixing all generate entropy. Reversing such processes exactly would require coordinated changes in the surroundings rather than simply running the equations backward.

Entropy is not energy

A system can conserve total energy while entropy increases. The second law therefore says something additional: energy becomes distributed among microscopic possibilities in ways that constrain how much organized work can be recovered.

Entropy gives a macroscopic measure of irreversibility and prepares the statistical interpretation in terms of microscopic states.