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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Thermodynamic Langevin equations.

Amilcare Porporato¹, Salvatore Calabrese², Lamberto Rondoni³

¹Department of Civil and Environmental Engineering and High Meadows Environmental Institute, <a href="https://ror.org/00hx57361">Princeton University</a>, Princeton, New Jersey 08540, USA.

Physical Review. E

|December 18, 2024

Summary

This summary is machine-generated.

This study explores generalized Gibbs ensembles, deriving nonlinear thermodynamic Langevin equations (TLEs) for macroscopic variables. It reveals distinct TLEs for macroscopic versus microscopic descriptions in small systems.

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Area of Science:

Statistical Mechanics
Non-equilibrium Thermodynamics
Small Systems Thermodynamics

Background:

Existing stochastic thermodynamics often links thermodynamic quantities to microscopic variables.
This work investigates stochastic variability directly within macroscopic variables of generalized Gibbs ensembles.
Focuses on thermodynamic fluctuations in small systems.

Purpose of the Study:

To scrutinize the physical significance of stochastic processes in generalized Gibbs ensembles.
To derive exact nonlinear thermodynamic Langevin equations (TLEs) for macroscopic variables.
To analyze the behavior of these TLEs for specific systems like ideal gases and colloidal particles.

Main Methods:

Recognizing the potential structure of Gibbs ensembles based on potential entropy generation.
Deriving nonlinear thermodynamic Langevin equations (TLEs) for macroscopic variables.
Analyzing canonical ensemble for ideal monoatomic gas and colloidal particle under constant force.

Main Results:

Exact nonlinear TLEs obtained for macroscopic variables, with drift expressed via entropic forces.
Analysis of ideal gas shows nonequilibrium heat transfer and bounds on entropy production.
For colloidal particles, macroscopic TLEs differ from microscopic ones, challenging standard stochastic thermodynamics assumptions.

Conclusions:

The derived TLEs offer a new perspective on thermodynamic fluctuations in small systems.
The approach provides a framework consistent with Hamiltonian mechanics, unlike some stochastic thermodynamics models.
Highlights the importance of considering macroscopic variables for accurate thermodynamic descriptions under non-equilibrium conditions.