Entropy production selects nonequilibrium states in multistable systems

Robert G Endres

doi:10.1038/s41598-017-14485-8

Abstract

Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to complicated physics, unintuitive stochastic thermodynamics, and the existence of alternative theories such as the minimum entropy production principle. Here, we use a simple, analytically solvable, one-dimensional bistable chemical system to demonstrate the validity of the maximum entropy production principle. To generalize to multistable stochastic system, we use the stochastic least-action principle to derive the entropy production and its role in the stability of nonequilibrium steady states. This shows that in a multistable system, all else being equal, the steady state with the highest entropy production is favored, with a number of implications for the evolution of biological, physical, and geological systems.

Highlights

The second law of thermodynamics is often misused to explain that life’s order, e.g. that of DNA, proteins, and cells, cannot emerge by chance[1]
With an interest in the emergence of protocells and life, we focus on stochastic biochemical systems and ask whether maximum entropy production principle (MaxEPP) provides a mechanism for selecting states in a multistable system
We demonstrate that previous attempts to disprove MaxEPP suffered from misinterpretations of unintuitive aspects of stochastic systems, and that with modern approaches in stochastic thermodynamics, MaxEPP can be proven

Summary

OPEN Entropy production selects nonequilibrium states in multistable systems

Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a longoutstanding puzzle. (this shows that small stochastic systems can violate the second law of thermodynamics!) At steady state, we again obtain the entropy production, and the ensemble averaged〈ΔSΓ(t)〉, averaged over trajectories Γ(t) of duration t, is given by the time-integrated entropy production rate[35]. In Eq (16), the sum is over reaction types, and the factor (w+r − w−r) and the log term represent the flux and the chemical-potential (or Gibbs free-energy) difference (divided by temperature T) of each reaction, respectively (see Supplementary Information for a derivation) This entropy production is illustrated, which shows both a low molecule-number state dissipating little, as well as a high-molecule number state dissipating a lot. MaxEPP is a principle for multistable systems in which the entropy production biases the evolution of the system towards the highest-entropy producing state

Discussion

Additional Information