Part VII: Thermodynamics and Entropy

The Observations

Entropy increases. Time flows in one direction. Heat flows from hot to cold. Processes are irreversible—you cannot unsqueeze toothpaste from a tube. Absolute zero (0 K) is unattainable. These observations constitute the second law of thermodynamics and define the arrow of time.

The Standard Interpretation

Statistical mechanics interprets entropy as a measure of microscopic configurations. Entropy increases because there are more disordered configurations than ordered ones; systems statistically evolve toward more probable states. The arrow of time is the direction of entropy increase. Absolute zero is the state of minimum entropy, unattainable because removing the last quantum of energy requires infinite effort.

The PSK Interpretation

PSK offers a geometric foundation for thermodynamics. Entropy increases because space is densifying—there is progressively more space, hence more possible configurations, hence higher entropy. This is not a statistical tendency that could, in principle, reverse. It is geometric necessity arising from the fundamental process of spatial densification.

The arrow of time is the direction of densification. We traverse from sparser to denser spatial states at rate c. The past (sparser states) no longer exists geometrically—those configurations are gone. The future (denser states) has not yet emerged. There is no backward because there is nothing to go back to.

Temperature as Density Offset

Consider a plot with spatial density on the y-axis (from ρ = 0 to ρ → ∞) and time on the x-axis (from t = −∞ to t = +∞). A line with slope c through the origin represents the baseline densification rate—the evolution of pure vacuum.

This baseline is absolute zero (0 K). Matter at absolute zero is perfectly synchronized with densification—progressing through density states at exactly rate c with no deviation.

Higher temperatures correspond to parallel lines with the same slope (c) but higher y-intercepts—offsets from the baseline. Matter at 293 K rides a line parallel to the 0 K baseline, offset by an amount corresponding to its thermal energy. All temperature states are parallel trajectories through the density-time plane, progressing at the same rate c, differing only in their offset from baseline.

Temperature is not how fast you traverse density states—everything traverses at c. Temperature is your offset from the minimum-entropy baseline.

Absolute Zero and Its Unattainability

Absolute zero corresponds to perfect synchronization with the baseline densification—zero offset, zero deviation, zero thermal energy. This is unattainable because any real matter has some structure, some internal dynamics, some offset from the pure vacuum baseline.

You can asymptotically approach the baseline but never reach it, because reaching it would mean your matter has no internal structure distinguishing it from empty space.

Irreversibility and Least Energy

When you squeeze a toothpaste tube, you do so while traversing into denser space. To unsqueeze would require the spatial configuration to return to what it was in a sparser state. But that state no longer exists geometrically. The configuration has moved on. Irreversibility is not statistical improbability; it is geometric impossibility.

Heat flows from hot to cold because systems resolve toward minimum energy configurations as they traverse densification. The densification process does not care about temperature offset—it proceeds regardless—but matter redistributes to minimize energy along the way. Higher-offset states adjacent to lower-offset states equilibrate because the combined system finds a lower-energy configuration.

This least-energy principle explains why planets are round (spheres minimize gravitational potential energy), why orbits are ellipses (minimum-energy stable trajectories), why electrons fill shells (minimum-energy atomic configurations). Everything finds the lowest-energy path through densification—not because a force pushes toward minimum energy, but because that is the path of least geometric resistance.

Unification

The second law of thermodynamics, the arrow of time, the irreversibility of processes, the direction of heat flow, and the universality of gravitational attraction are revealed as aspects of the same geometric phenomenon: space densifies, matter traverses into denser states, configurations resolve toward minimum energy, and the past ceases to exist.