Tuesday 26 March 2013

Language and Spacetime Time Flow in Word For KOHARI Akihiro and His Time




Time Flow in Word

For KOHARI Akihiro and His Time


1
Word is expressed by phase space in the situation on dynamical system.
Phase space M has a point x.
Continuous time t is expressed by group R that consists of real number.
Homomorphism φt(x)expresses the system.
φs+t(x) =φs (φt(x)), φ(x) = x
2
In thermodynamics, equilibrium is presented.
Equilibrium situation is expressed by (U, V, n).
U is energy in the system. V is volume. n is material.
Here new equilibrium is expressed by (U’, V’, n).
3
Now a category is presented.
(U, V, n) (U’, V’, n)
f is function of entropy.
Here (U, v, n) is expressed by P. (U’, V’, n) is expressed by P’.
The situation of equilibrium is expressed by the following.
: P  P’
4
The situation of equilibrium is rewritten by phase space.
Each situation of equilibrium is expressed by a point x.
After time t, point x and x’ is presented by the following.
φ : φs(x) φs+t(x)
5
Now equilibrium system is expressed by {φt} that is called flow.
Here phase space M can take tangent vector X.
Point x has tangent vector X= dφt(x)/dtt=0
The flow has solution as equation φt(x)/dt = Xφt(x)
6
Here set {φt(x) | tR } is presented. The set is called orbit.
7
In word, meaning is expressed by flow and time is expressed by orbit.

Tokyo May 3, 2007

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