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Thomas Dittrich¹, Santiago Peña Martínez¹

¹Departamento de Física, Universidad Nacional de Colombia, Bogotá 111321, Colombia.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

We model discrete randomness in bistable systems. Increasing environmental complexity (N) leads to relaxation, not chaos, with outcomes determined by initial conditions.

Keywords:

bistability chaos double well finite heat bath fluctuations irreversibility randomness relaxation spin-boson model

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Area of Science:

Statistical Mechanics
Nonlinear Dynamics
Quantum Chaos

Background:

Bistable systems exhibit complex dynamics when coupled to environments.
Understanding discrete randomness is crucial for modeling emergent behavior.

Purpose of the Study:

To investigate the transition from integrable to chaotic dynamics in a bistable system.
To explore the role of environmental degrees of freedom (N) in system relaxation.
To reconcile symmetry in initial conditions with spontaneous symmetry breaking in the final state.

Main Methods:

Microscopic model construction with a quartic double well coupled to N harmonic oscillators.
Numerical solution of time-reversal invariant Hamiltonian equations of motion.
Analysis of autocorrelation, partial entropy, and inter-well jump frequency as functions of N.

Main Results:

For N=1, a transition from integrable to chaotic motion occurs with increasing coupling strength (Kolmogorov-Arnol'd-Moser scenario).
For N >= 10, dynamics shift to quasi-relaxation towards stable equilibria.
System relaxation outcomes are reproducibly determined by initial bath asymmetries, despite overall symmetry.

Conclusions:

Environmental complexity drives bistable systems towards relaxation rather than sustained chaos.
The model reconciles macroscopic irreversibility and symmetry breaking with microscopic time-reversal invariance.
Residual initial asymmetries dictate the direction of spontaneous symmetry breaking.