iSoul In the beginning is reality.

A dual of the second law of thermodynamics

This is a continuation of the series of posts on the duality of space and time. Consider an isolated system of particles over a period of time. The system covers a specific distance in space and a specific duration in time. Consider only one dimension of space and one dimension of time with an origin point.

The second law of thermodynamics says that the entropy of the distribution of particles at each timepoint over the space tends to increase with increasing duration. Call this the s-entropy since the distribution is over space. What about the distribution of particles at each point of space over the time period? Call this the t-entropy (time entropy).

Consider different scenarios. If the system is at equilibrium, there will be no change over time and the distribution will be constant, which would be the minimum t-entropy, that is, zero. If the system is near equilibrium, there will be little change over time and the distribution will be near constant, which would be a low t-entropy. If the system is far from equilibrium, i.e., the particles are bunched up together, the system will change toward equilibrium.

The tendency is for small intervals of time with many particles to end up with fewer particles, and small intervals of time with few particles to end up with more particles. If the origin is near the concentration of particles, the t-entropy of the distributions of particles in time over space will tend to decrease. If the origin is away from the concentration of particles, the t-entropy of the distributions of particles in time over space will tend to increase.

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