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Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
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Updated: Jun 8, 2026

Following the Dynamics of Structural Variants in Experimentally Evolved Populations
04:52

Following the Dynamics of Structural Variants in Experimentally Evolved Populations

Published on: February 3, 2023

Evolutionary dynamics from a variational principle.

Peter Klimek1, Stefan Thurner, Rudolf Hanel

  • 1Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, A 1090 Vienna, Austria.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Evolutionary systems cannot be predicted by fitness alone due to new species. A new variational principle offers a functional to derive evolutionary trajectories and predict species diversity.

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Area of Science:

  • Evolutionary biology
  • Theoretical ecology
  • Complex systems

Background:

  • Fitness-based population dynamics struggle with long-term evolutionary predictions.
  • The endogenous production of new species continuously alters ecological conditions.
  • Fitness is an outcome, not an explanation, of reproductive success.

Purpose of the Study:

  • To address limitations of fitness-based models in evolutionary systems.
  • To propose a novel variational principle for evolutionary dynamics.
  • To enable quantitative, falsifiable predictions of evolutionary system behavior.

Main Methods:

  • A thought experiment challenging current evolutionary approaches.
  • Development of a variational principle within a spin-model-like framework.
  • Derivation of a minimized functional governing evolutionary trajectories.
  • Mean-field approximation for asymptotic diversity in stochastic systems.

Main Results:

  • Evolutionary trajectories emerge as a minimization of a derived functional.
  • Analytic solutions for asymptotic diversity in stochastic systems were obtained.
  • Numerical simulations confirmed good agreement with model predictions, especially phase transitions.
  • The model successfully reproduces empirical data from natural and man-made systems.

Conclusions:

  • A new theoretical framework overcomes limitations of fitness-based evolutionary models.
  • The proposed functional provides a predictive tool for evolutionary system dynamics.
  • This approach sheds light on the coevolution of species and their fitness landscapes.