PATMO has been developed to compute time-dependent averaged entropy production.
Standard entropy production of the jth reaction is defined as (see Chapter 9 in: Kondepudi, D., Prigogine, I., Modern Thermodynamics: From Heat Engines to Dissipative Structures)
where R is the gas constant, and F_f and F_b are the forward and backward reaction fluxes, respectively, i.e.
where the product is over the number densities of the reactants, and k is the reaction rate coefficient.
We can average the fluxes over time as
The entropy production can be then defined as
where we omitted the reaction index j.
You can compute entropy production with the two functions described here below.
Computes entropy production in a time-step dt.
This subroutine sum the fluxes of all the rates in the given dt, but it doesn't actually compute the entropy production to avoid division by zero.
See patmo_getEntropyProduction function.
Pseudocode here below:
do loop on time with timestep dt
call patmo
time = time + dt
call patmo_computeEntropyProductionFlux(dt)
end do
print "entropy production:", patmo_getEntropyProduction(time)
Computes and returns the average entropy production in the given time interval.
To be used at the end of the run after calling patmo_computeEntropyProductionFlux (see).
Since the definition of averaged entropy production is
clearly, when <F_b> is very small this quantity can easily diverge.
This is typical when a reaction is far from the equilibrium and when its time-scale is extremely long.
To have a control on this a warning message is displayed when patmo_getEntropyProduction is called, and it looks like
WARNING: suspiciously low Reverse/Forward flux ratio for rates:
17
32
70
77
where the numbers are the indexes of the rates that present this problem.
This file produced when patmo_getEntropyProduction function is called has the following header
#cell_number reaction_index contribution_to_entropy Rb/Rf
where Rb/Rf (that is <F_b>/<F_f>) allows to evaluate if each contribution to entropy is "trustable" or not according to what discussed in the section above.
