Covariant Non-equilibrium Thermodynamics from Ito-Langevin Dynamics

Abstract

Using the recently developed covariant Ito-Langevin dynamics, we develop a non-equilibrium thermodynamic theory for small systems coupled to multiplicative noises. The theory is based on Ito-calculus, and is fully covariant under time-independent nonlinear transformation of variables. Assuming instantaneous detailed balance, we derive expressions for various thermodynamic functions, including work, heat, entropy production, and free energy, both at ensemble level and at trajectory level, and prove the second law of thermodynamics for arbitrary non-equilibrium processes. We relate time-reversal asymmetry of path probability to entropy production, and derive its consequences such as fluctuation theorem and non-equilibrium work relation. For Langevin systems with additive noises, our theory is equivalent to the common theories of stochastic energetics and stochastic thermodynamics. We also discuss examples of multiplicative noises where the common theories are inapplicable, but our theory yields correct results.

arXiv comment22 pages

References in corpus (15)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• First and Second Law of Thermodynamics at strong coupling
• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Entropy production in full phase space for continuous stochastic dynamics
• Anomalous thermodynamics at the micro-scale
• The Fluctuation Theorem for Stochastic Systems
• Non-equilibrium thermodynamics of stochastic systems with odd and even variables
• Multiple-scale stochastic processes: decimation, averaging and beyond
• Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
• Functionals in stochastic thermodynamics: how to interpret stochastic integrals
• Comment on "Irreversibility and Fluctuation Theorem in Stationary Time Series"

Cited by in corpus (2)

• Strong Coupling Thermodynamics and Stochastic Thermodynamics from the Unifying Perspective of Time-Scale Separation
• Time-Slicing Path-integral in Curved Space