Entropy production and volume contraction in thermostated Hamiltonian dynamics

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Physics

Background:

• Previous studies showed equality between entropy production and phase-space volume contraction rates in specific molecular dynamics methods.
• This equality serves as a statistical analog to the second law of thermodynamics in nonequilibrium steady states.
• Hamiltonian systems with thermostated temperature gradients are crucial for these simulations.

Purpose of the Study:

• To demonstrate the identical equality of entropy production and phase-space volume contraction rates.
• To extend the validity of this equality to a broader class of molecular dynamics methods.
• To reinforce the connection between simulation dynamics and thermodynamic principles.

Main Methods:

• Analysis of molecular dynamics methods for simulating nonequilibrium steady states.
• Focus on methods where thermostat variables are governed by ordinary differential equations.
• Identification of three general restrictions typically satisfied by these methods.

Main Results:

• The time-averaged rates of entropy production and phase-space volume contraction are shown to be identically equal.
• This equality holds for a wide class of thermostatting methods, including Nosé-Hoover and integral feedback control types.
• The identified restrictions are generally met in these commonly used simulation techniques.

Conclusions:

• The demonstrated identical equality provides robust support for the statistical analog of the second law of thermodynamics.
• The findings broaden the applicability of this thermodynamic principle in computational simulations.
• This work enhances the theoretical understanding of thermostatting algorithms in molecular dynamics.