Dissipative adaptation vs. principle of least entropy production I am interested in Jeremy England's non-equilibrium thermodynamic theory of "dissipative adaptation".  See refs like https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.119.038001.
My understanding of his theory is that systems, when driven out of equilibrium, tend to organize themselves such that dissipation of energy from the driving forces becomes large.
However, my understanding of Prigogine's main result is that Onsager's reciprocal relations lead one to the conclusion that systems driven  slightly out of equilibrium (i.e. in a regime where Onsager's linearized theory is valid) will come back to equilibrium in a way that minimizes the rate of entropy production. 
Now these two notions sound opposite to me; England's theory of maximum dissipation sounds like a maximization of entropy production.  Do I have this wrong?  Or is the crucial difference simply the realm of applicability of the two theories (far from equilibrium, in England's case, or near equilibrium, in Prigogine's case)?
 A: "England's theory of maximum dissipation sounds like a maximization of entropy production. Do I have this wrong?"
Short answer
In short this theory implies maximization of entropy production
in some cases and minimization in others.
Long answer (as I understand the paper)
One of the main results of J. England paper [ 1 ] is the equation (11)
I post it here it in a more explicit way
$$
\begin{split}
  \ln
  \left[
    \dfrac{
      \pi \left(
        \textbf{I} \rightarrow \textbf{II}; \tau
      \right)
    }{
      \pi \left(
        \textbf{I} \rightarrow \textbf{III}; \tau
      \right)
    }
  \right]
  =
  &\underbrace{
  -
  \ln
  \left[
    \dfrac{
      \left\langle
        \frac{ p(x | \textbf{II}, \textbf{I}; \tau)}{
            p_{bz}(x|\textbf{II})
          }
      \right\rangle_{\textbf{II}}
    }{
      \left\langle
        \frac{ p(x | \textbf{III}, \textbf{I}; \tau)}{
          p_{bz}(x|\textbf{III})
        }
      \right\rangle_{\textbf{III}}
    }
  \right]
  }_{\text{"distance" from thermodynamic equilibrium}}
  +
  \underbrace{
  \ln
    \left[
      \dfrac{
        \pi \left(
          \textbf{II} \rightarrow \textbf{I}; \tau
        \right)
      }{
        \pi \left(
          \textbf{III} \rightarrow \textbf{I}; \tau
        \right)
      }
    \right]
  }_{\text{reverse transition}}
  +
  \\
  &+\underbrace{
  \left(
%     \Delta\Psi_{\textbf{II, III}}^{\textbf{I}, \text{fwd}}
    \Psi_{I \rightarrow II} - \Psi_{I \rightarrow III}
  \right)
  }_{\text{average dissipation}}
  -
  \underbrace{
%     \Delta\Phi_{\textbf{II, III}}^{\textbf{I}, \text{fwd}}
    \left(
      \Phi_{I \rightarrow II}
      -
      \Phi_{I \rightarrow III}
    \right)
  }_{\text{fluctuations of disipation}}
\end{split}
$$
As you can see this equation can imply maximization of entropy production as
well as minimization of it.
Dissipative adaptation implies both (minimization and maximization of dissipated work)
Assumptions
1.
For simplicity let's ignore first two terms (I am not sure weather this is a safe assumption)
$$
\underbrace{
-
\ln
\left[
  \dfrac{
    \left\langle
      \frac{ p(x | \textbf{II}, \textbf{I}; \tau)}{
          p_{bz}(x|\textbf{II})
        }
    \right\rangle_{\textbf{II}}
  }{
    \left\langle
      \frac{ p(x | \textbf{III}, \textbf{I}; \tau)}{
        p_{bz}(x|\textbf{III})
      }
    \right\rangle_{\textbf{III}}
  }
\right]
}_{\text{"distance" from thermodynamic equilibrium}}
+
\underbrace{
\ln
  \left[
    \dfrac{
      \pi \left(
        \textbf{II} \rightarrow \textbf{I}; \tau
      \right)
    }{
      \pi \left(
        \textbf{III} \rightarrow \textbf{I}; \tau
      \right)
    }
  \right]
}_{\text{reverse transition}}
=0
$$


*Assume that the during the transition
$\textbf{I} \rightarrow \textbf{II}$ the system
(on average) disipated more work than during the transition $\textbf{I} \rightarrow \textbf{III}$:
$$
  \Psi_{I \rightarrow II} - \Psi_{I \rightarrow III} > 0
$$


i.e. state $\textbf{II}$ is in "direction" of maximization of entropy production.
Maximization of entropy production case
Assume this inequality
$$
  \underbrace{
  %     \Delta\Psi_{\textbf{II, III}}^{\textbf{I}, \text{fwd}}
    \Psi_{I \rightarrow II} - \Psi_{I \rightarrow III}
  }_{\text{difference of average dissipation}}
  >
  \underbrace{
  %     \Delta\Phi_{\textbf{II, III}}^{\textbf{I}, \text{fwd}}
      \Phi_{I \rightarrow II}
      -
      \Phi_{I \rightarrow III}
  }_{\text{difference of fluctuations of disipation}}
$$
this implies
$$
\pi \left(
  \textbf{I} \rightarrow \textbf{II}; \tau
\right)
>
\pi \left(
  \textbf{I} \rightarrow \textbf{III}; \tau
\right)
$$
System is more likely to choose a transition of more average dissipation.
In other words: if the transition to a macro-state has high work dissipation and little fluctuations
around average dissipation then (ignoring first two terms of eq. 11) the system is going to optimize to dissipate more work.
Minimization of entropy production case
Assume this inequality
$$
\underbrace{
%     \Delta\Psi_{\textbf{II, III}}^{\textbf{I}, \text{fwd}}
  \Psi_{I \rightarrow II} - \Psi_{I \rightarrow III}
}_{\text{difference of average dissipation}}
<
\underbrace{
%     \Delta\Phi_{\textbf{II, III}}^{\textbf{I}, \text{fwd}}
    \Phi_{I \rightarrow II}
    -
    \Phi_{I \rightarrow III}
}_{\text{difference of  fluctuations of disipation}}
$$
this implies
$$
\pi \left(
  \textbf{I} \rightarrow \textbf{II}; \tau
\right)
<
\pi \left(
  \textbf{I} \rightarrow \textbf{III}; \tau
\right)
$$
System is more likely to choose a transition of less average dissipation.
Both cases according to the paper [2]
Authors have observed both cases in this paper [2]
(see supplementary material
)
"Simulations of our model using these different rate rules gave, broadly, results reversed relative to those reported in the main text. Strikingly, the spectrum of such systems showed a suppression effect in frequencies around the driving frequency. An example of this effect is illustrated in Figure S8. Furthermore, the projection of the force vector in the normal mode basis shows that the same frequencies also tend to decouple from the drive."

Figure S8 [2].
"
Distribution of natural frequencies for the driven system ($_=1.5$) with bonds that “catch” (red), compared to the same with bonds that “snap” (green) and the undriven system (blue)."
We see that a system with one type of toy chemical bonds (red line)
optimizes to dissipate more work and the other
system with different chemical bonds (green line) omptimizes to dissipate less work.
Literature


*

*PERUNOV, Nikolay; MARSLAND, Robert A.; ENGLAND, Jeremy L. Statistical
physics of adaptation. Physical Review X, 2016, 6.2: 021036.

*KACHMAN, Tal; OWEN, Jeremy A.; ENGLAND, Jeremy L. Self-Organized Resonance during Search of a Diverse Chemical Space. Physical Review Letters, 2017, 119.3: 038001.
