Authors: Alexandre Harvey-Tremblay
Here we introduce a non-commutative extension to statistical physics granting it the ability to associate an entropy to arbitrary space-times. Generally speaking, statistical physics connects a set Q of 'microstates' (a.k.a the microscopic description) to a set of functions on Q (a.k.a. the bulk state) by the use of Lagrange multipliers, and under the principle of maximum entropy. In the present case, the 'microscopic' object of study is the space-time event, the bulk state is the space-time curvature, and the Lagrange multiplier is the speed of light. A partition function of such events can be constructed by using generators of the Clifford algebra. These generators ascribe geometric properties to the equation of state of such a system. Finally, the Einstein field equations are obtained by applying the principle of stationary action to the equation of state. The framework provides numerous new insight regarding the passage of time; for instance, the arrow of time becomes an arrow of space-time, and also from an entropy standpoint; specifically, the future is the region of space-time hidden from the observer by an entropy. We end the paper with a discussion of these insights.
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