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Published on: December 4, 2017
Irreversible thermodynamics in multiscale stochastic dynamical systems.
1Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Unidad Monterrey, Parque de Investigación e Innovación Tecnológica, 66600 Apodaca, Nuevo León, Mexico. msantillan@cinvestav.mx
Summary
This study reveals how fast dynamics in multiscale stochastic systems affect thermodynamic properties. Free energy remains invariant, but entropy and internal energy are influenced by faster processes.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Stochastic Processes
Background:
- A recently developed thermodynamic formalism for Markov processes is extended.
- Investigating thermodynamic structure invariance in multiscale stochastic systems is crucial for understanding complex dynamics.
Purpose of the Study:
- To determine if thermodynamic structure is invariant across different time scales in multiscale stochastic systems.
- To analyze the impact of fast dynamics on thermodynamic state and process variables in slow dynamics.
Main Methods:
- Analysis of discrete-state, continuous-time Markov processes.
- Application of a thermodynamic formalism considering detailed balance and its absence.
- Investigation of time-scale separation and its consequences.
Main Results:
- Fast dynamics contribute an entropic term to the internal energy of slow dynamics.
- Conditional free energy allows treating slow dynamics independently of fast dynamics.
- Free energy is invariant to fast dynamics, while entropy and internal energy are affected.
Conclusions:
- Time-scale separation in multiscale systems leads to specific contributions to thermodynamic functions.
- The invariance of free energy simplifies analysis of spontaneous organization.
- Understanding these scale-dependent effects is key for phenomenological steady-state thermodynamics.
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