Steady-state distributions and nonsteady dynamics in nonequilibrium systems

Area of Science:

• * Non-equilibrium statistical mechanics
• * Theoretical physics
• * Complex systems

Background:

• * Traditional steady states apply to systems at thermodynamic equilibrium.
• * Fluctuating and driven systems present challenges to equilibrium concepts.
• * Sustained currents in these systems indicate non-equilibrium behavior.

Purpose of the Study:

• * To generalize the concept of a steady state for driven, fluctuating systems.
• * To identify conditions for the existence and stability of these generalized steady states.
• * To provide a theoretical framework for analyzing non-equilibrium currents.

Main Methods:

• * Analysis of probability density functions for system microstates.
• * Modeling of deterministic dynamical systems representing average trajectories.
• * Derivation of conditions for steady-state existence and stability.

Main Results:

• * A generalized steady state is characterized by a stationary probability density.
• * System trajectories on average follow a deterministic dynamical system.
• * Precise conditions for the existence and stability of this generalized steady state were determined.

Conclusions:

• * The concept of steady state requires generalization beyond equilibrium conditions.
• * Generalized steady states are essential for describing systems with sustained currents.
• * The findings provide a robust framework for studying non-equilibrium physical phenomena.