The Duality of Time Theory

Clausius also realized that heat engines could utilize only some of the available heat to do work, and from this he developed the concept of entropy, which he showed that it always increased in any spontaneous natural process. This in turn established the second law of thermodynamics, which states that, in isolated systems, the total entropy can only increase over time.

Entropy is related to the number of microscopic configurations that a thermodynamic system can have when in a state as specified by some macroscopic variables. Assuming for simplicity that each of the microscopic configurations is equally probable, the entropy of the systemis the natural logarithm of that number of configurations, multiplied by Boltzmann constantwhich has the dimension of energy divided by temperature:

In the modern microscopic interpretation of entropy in statistical mechanics, entropy is the amount of additional information needed to specify the exact physical state of a system, given its thermodynamic specification.

The second law of thermodynamics is one of the fundamental laws of nature. After developing General Relativity, in the 1920s, many theoretical physicists, including Einstein, considered the possibility of cyclic models in which the universe follows indefinite self-sustaining cycles of eternal series of expansion and contraction. We shall briefly discuss these models in chapter III.

Another important puzzle associated with the second law of thermodynamics is the entropic arrow of time, because it requires a particular direction for time, unlike most other laws of physics which are time-symmetric. The Arrow of Time concept was developed by Arthur Eddington (1882-1944 AD) in 1927 and it is still an unsolved general physics problem. as we indicated in chapter I and will discuss further in chapter V, the Duality of Time is intrinsically built on one time direction, both for the inner and outer levels, and the arrow of time will be explicitly expressed in the equations that will also show how two opposite arrows of time combine to make one (two-directions) dimension of space. We will also discuss the entropic and other similar arrows of time that result from various other natural phenomena when we review modern physics and cosmology in chapter III.