The entropy of systems

It depends in which papers you read.

The study of dissipative systems are very much of interest these days as it is in quantum dynamics for example:

arxiv.org/PS_cache/quant-ph/pdf/0511/0511091v3.pdf

The "relaxation" of the atoms in any body at the surface of the earth is caused by the energy variation within the whole mass of the earth.

One can write the equation F = dp/ dt in terms of changing energy (which is the same as changing mass)

GD: 31 Jul 2009 : 19:38:50<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">It depends in which papers you read.

The study of dissipative systems are very much of interest these days as it is in quantum dynamics for example:

arxiv.org/PS_cache/quant-ph/pdf/0511/0511091v3.pdf
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">What do you mean by "it"? I thought we were talking about mass, but the word "mass" does not appear in the paper you referenced. Nor does the word "force" appear in that paper. Are you changing the topic back to entropy before or after that opening sentence?

Are you just trying to impress us by posting a link to a paper that we can't understand? (Did you understand that paper, Larry?) I <b>will</b> be impressed if you can explain it so that I <b>can</b> understand it. Bear in mind, I am not a mathematician, so please use plain English.

Fractal Foam Model of Universes: Creator

Dissipative systems has to do with changing mass...
There is lots of info on this on the web.

Here is a concluding remark at the end of the paper:

"The growing interest during the last several decades
in quantum dynamical models of systems undergoing irreversible
processes has been motivated by impressive
technological advances in the manipulation of smaller
and smaller systems, from the micrometer scale to the
nanometer scale, and down to the single atom scale."

"...In this paper, we consider a class of model evolution
equations applicable not only to open systems but also
to closed isolated systems, capable of describing, simultaneously
with the usual Hamiltonian unitary evolution,
the natural tendency of any initial nonequilibrium state
to relax towards canonical or partially-canonical thermodynamic
equilibrium, i.e., capable of describing the irreversible
tendency to evolve towards the highest entropy
state compatible with the instantaneous mean values of
the energy, the other constants of the motion, and possibly
other constraints...

The equation starts: dp/ dt (change in quantum state with changing time) This is how mass (energy) variation occurs.

GD: 01 Aug 2009 : 10:56:07<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">The equation starts: dp/ dt (change in quantum state with changing time) This is how mass (energy) variation occurs.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">It is beginnig to become clear where some of our disagreements are coming from. It is confusion over what certain letters stand for. Beretta (the paper's author) is really stingy with explanations of what his symbols represent. Although some of his formulas look similar to F = dp/dt, they are not even related, as far as I can tell, to "force = rate of change of momentum". He never explains what "F" represents; is it force? I have been able to determine that he uses "p" to represent probability, not momentum, and his Greek letter "rho" is the " density operator ", which represents a matrix.

I vaguely recall a simester of matrix algebra in high school, some 45 years ago. Apparently, there's a lot of matrix related nomenclature in Beretta's writing, and he assumes that his audience knows what it all means; <i>but for mine own part, it was <b>Geek</b> to me.</i>

Fractal Foam Model of Universes: Creator

...trying to understand Beretta's equations:

Density matrix:
"...It is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical mechanics."

... The "Hamiltonian" equations replaces the usual equations used in mechanics (based on forces) with equations expressed in terms of momenta]

Momentum:
"...is the product of the mass and velocity of an object (p = mv).
Momentum is a conserved quantity, meaning that the total momentum of any closed system (one not affected by external forces) cannot change. This law is also true in special relativity."

Newton's law of motion:
"The change of momentum of a body is proportional to the impulse impressed on the body,..."

definition of impulse :
The product of a force and duration (time) it is applied. If the force is variable,the impulse is the integral of Fdt from t0 to t1. the impulse of a force acting for a given time interval is equal to the change in momentum produced over that interval. (Here it is assumed that mass is constant)
Impulse: Fdt = mdv = dP (momentum) when force and mass are constant

If mass is not constant:

Specific impulse:
is an impulse per unit mass, which dimensional analysis shows to be a unit of speed, and so specific impulses are often measured in meters per second. However, if weight is used instead, an impulse divided by a force (weight) turns out to be a unit of time, and so specific impulses are measured in seconds. These two formulations are both widely used, and differ from each other by a factor of g, the dimensioned constant of gravitational acceleration at the surface of the Earth.

When force and mass are not constant: (GD: in rocketry, qty of mass required to be converted into energy to produce a force to escape from the gravitational pull of the attractor_ ie: center of the earth)

Specific impulse as measured in sec:
F variable = I sp (dm/dt) g0

F, Force measured in newtons
I sp, specific impulse measured in seconds
g0 is the acceleration at the earths surface measured in m/s^2

Specific impulse can also be measured in meters/ sec:
I sp = Ve / g0

Ve measured in m/s
I sp measured in seconds
g0 is the acceleration at the earths surface measured in m/s^2

PhilJ:

Force is part of Beretta's equations.

Beretta's paper explains the evolution of a system. Forces, mass (mass density ,energy field density, flux density... all the same), vary with time.
Newton's equation F=ma does not show this. Mass remains constant.
dp/dt in his paper (I believe) is the change in density of a mass with time...

I suspect that Gravity is the relaxation of energy state within a body. Changing a mass from something which has internal energy to something which does not (energy dissipation to the environment) . Basically changing a mass (or energy) density of a body from an atom into its basic subatomic particles.
The changing rate of energy dissipation would vary the momentum of a body.

The best term I found which explains this is impulse (constant mass) probably caused by: specific impulse (variable mass).

According to you, what is Beretta trying to show by integrating the second law of thermodynamics, and the changing density of a mass ?
Does the universe need to be a closed system so that motion is conserved?
(motion is conserved in a closed system).

How is motion conserved? With constant mass or varying mass?
Doesn't the second law of thermodynamics imply varying mass?

<i>... edited ...
I replaced "momentum" by "motion" in the last two sentences. The rate of momentum changes continually (the reason for the acceleration of bodies).
Therefore P=mv does not describe the motion of bodies in the universe.</i>

Would anyone like to use my registration to go to Walter Cruttenden's "Conference on Precession and Ancient Knowledge (CPAK)", October 10, 2009 (a one day event, a week from this Saturday) at the Univ. of California-Irvine? I've paid the $179 registration but can't go. You would have one duty for me there: to check that my poster stays up (I'll lend you a spare, so you can replace my poster if you notice it gets ripped off).