Stochastic Dynamics in Non-Equilibrium Thermodynamic Systems

Overview

When a classical, ideal thermodynamic system is driven from equilibrium, it tends towards maximal entropy, described by the Boltzmann distribution. However, the probability distribution of a non-equilibrium system does not always approach the Boltzmann distribution without first showing preference for configurations that are not a simple interpolation between where the system is now and where it will be at equilibrium. In this work, we investigate what conditions allow for these deviations to arise. We model the system using a Markov process. Two paths are offered to the system from an initial low entropy state: one’s evolution is a simple interpolation between the initial state and the final Boltzmann distribution. The other involves the preference of a state which happens to be more efficient at dissipating free energy. The transition probabilities between states are determined by the Crooks fluctuation theorem. The latter path takes the system temporarily farther from equilibrium because of its preference of a specific configuration. Nevertheless, the greater dissipation ultimately increases entropy at a greater rate than the first alternative. We demonstrate that certain states are preferred when there is an accompanying increase in entropy production at the global scale, as in the second path. This is generally applicable to any system which does not experience an isotropic increase of entropy in all regions of the system. Finally, the broader relevance of this topic is discussed, including possible analogies between a tendency towards particular states in a Markov process and the emergence of complexity in the natural world.

Competition history

• AJAS 2018 Category not listed

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