Learning stochastic thermodynamics directly from correlation and trajectory-fluctuation currents

Area of Science:

• Statistical Physics
• Machine Learning
• Dynamical Systems

Background:

• Growing interest in data-driven inverse dynamics problems requires managing noise in complex systems.
• Stochastic dynamics, particularly Langevin dynamics, are crucial for modeling systems interacting with environments.
• Currents are gaining attention for bounding entropy production via thermodynamic uncertainty relations (TURs).

Purpose of the Study:

• To develop a learning framework for stochastic modeling using currents.
• To establish a relationship between cumulant currents and machine learning loss functions.
• To derive loss functions for thermodynamic quantities directly from system dynamics.

Main Methods:

• Constructing a learning framework for stochastic modeling using currents.
• Establishing a fundamental relationship between cumulant currents and standard machine-learning loss functions.
• Deriving loss functions for key thermodynamic functions directly from system dynamics.

Main Results:

• Derived loss functions that reproduce results from TURs and other methods.
• Enabled discovery of new loss functions for previously inaccessible quantities, including per-trajectory entropy production.
• Demonstrated a straightforward method unifying dynamic inference with entropy production estimation.

Conclusions:

• A deep connection exists between diffusion models in machine learning and entropy production estimation in stochastic thermodynamics.
• The framework provides direct access to thermodynamic quantities, even for systems far from steady state.
• This approach simplifies dynamic inference and entropy production estimation.