Nonequilibrium Entropic Bounds for Darwinian Replicators
Abstract
:1. Introduction
2. Entropic Bounds for Replicators
2.1. The Extended Second Law
2.2. Replicators & Reproducers
2.3. Coarse-Grained Dynamics of Replicators
- —state in which the system contains a total number of active chains.
- —state in which the system contains a total amount of n active chains.
3. Discussion
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
MDPI | Multidisciplinary Digital Publishing Institute |
DOAJ | Directory of open access journals |
ESL | Extended Second Law |
LEB | Lower Entropic Bound |
LHS | Left Hand Side |
RHS | Right Hand Side |
Appendix A
Appendix B
Appendix B.1
- Pick an element of the urn at random.
- If active, with probability g, pick a second element at random and (if not active) activate.
- Pick an element at random again.
- If active, with probability , deactivate.
Appendix B.2
- Pick an element of the urn at random.
- If active, pick a second element at random.
- If active, with probability h, pick a third element at random and (if not active) activate.
- Pick an element at random again.
- If active, with probability , deactivate.
Appendix B.3
- Pick an element of the urn at random. If active, then: (i) if in associated state () then, with probability a, dissociate and iterate; (ii) if dissociated, pick a second element and, if active, with probability b, associate. Iterate this process until equilibrium is reached for association/dissociation reaction.
- Pick an element of the urn at random. If active, pick a second element at random, if empty, with probability c, replicate.
- Pick an element of the urn at random. If active, with probability , deactivate.
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Replicator Class | Reaction Scheme | Effective Dynamics |
---|---|---|
Simple | ||
Hyperbolic | ||
Parabolic |
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Piñero, J.; Solé, R. Nonequilibrium Entropic Bounds for Darwinian Replicators. Entropy 2018, 20, 98. https://0-doi-org.brum.beds.ac.uk/10.3390/e20020098
Piñero J, Solé R. Nonequilibrium Entropic Bounds for Darwinian Replicators. Entropy. 2018; 20(2):98. https://0-doi-org.brum.beds.ac.uk/10.3390/e20020098
Chicago/Turabian StylePiñero, Jordi, and Ricard Solé. 2018. "Nonequilibrium Entropic Bounds for Darwinian Replicators" Entropy 20, no. 2: 98. https://0-doi-org.brum.beds.ac.uk/10.3390/e20020098