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Re: [Phys-l] physics of dissipation (was: T dS versus dQ)

Hi Chuck,

Yes. Time becomes meaningful in non-equilibrium thermodynamics. General case is described below:

Adapted from: "The Residence Time of Energy as a Measure of Ecological Organization" E.F Cheslak and V. A. Lamarra (1981) in Energy and Ecological Modelling, who references Morowitz (1968) Energy Flow in Biology, and Glasstone et. al. (1941) The Theory of Rate Processes.

Helmholtz free energy

A = U - TS

is minimized when entropy is at a maximum.

Difference between non-equilibrium and equilibrium value is measure of departure from equilibrium, so:

delta A(T') = A(T')@nonequilibrium - A(T')@equilibrium

Normalizing by introducing an order function, which incorporates energy storage and flow,

L = h delta A(T') / kT'

which represents a ratio of an energy to a rate, describing decay to equilibrium. Cheslak et. al. conclude that this represents order in the system, and go on to apply this in macroscopic biological systems, using an energetic residence time.

An energetic residence time is also useful in transportation analysis, as shown here:

Jeff Radtke, Supersaturated Environments
who thinks S. Glasstone is the best science writer, ever.

Quoting chuck britton <>:

and now - really stretching here - is there any generalization that
relates to the recent (short lived) discussion of 'Residence Time').