Microscopic reversibility and heat for thermostatted systems

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Physical Chemistry

Background:

• Hamiltonian dynamics describes time-reversible systems.
• Thermostatted dynamics, like Nose-Hoover, introduce dissipation.
• Universality of symmetries in different dynamic systems is an open question.

Purpose of the Study:

• To investigate the universality of a known symmetry in Hamiltonian dynamics.
• To examine if this symmetry persists in Nose-Hoover thermostatted dynamics.
• To explore the implications of this symmetry for open systems and thermodynamics.

Main Methods:

• Analyzing trajectories from Nose-Hoover thermostatted dynamics.
• Comparing the observed symmetry with that of Hamiltonian dynamics.
• Applying the identified symmetry to understand microscopic reversibility.

Main Results:

• The study found that the same symmetry observed in Hamiltonian dynamics holds for Nose-Hoover thermostatted dynamics.
• This symmetry persists despite the presence of dissipation and phase volume contraction.
• Microscopic reversibility for open systems was demonstrated using this symmetry.

Conclusions:

• A fundamental symmetry is universal across both conservative (Hamiltonian) and dissipative (thermostatted) dynamics.
• This universality provides a bridge between the first and second laws of thermodynamics for open systems.
• The findings offer a deeper understanding of the behavior of open systems in statistical mechanics.