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Entropy production rate and time-reversibility for general jump diffusions on RRn
1Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China.
Chaos (Woodbury, N.Y.)
|October 1, 2025
Summary
This study explores entropy production and time-reversibility in jump diffusions (Lévy processes). We found that time-reversibility is equivalent to zero entropy production and detailed balance for stationary jump diffusions.
Area of Science:
- Stochastic Processes
- Non-equilibrium Thermodynamics
- Mathematical Physics
Background:
- Jump diffusions, also known as Lévy processes, are crucial in modeling complex systems with discontinuous dynamics.
- Understanding entropy production is fundamental to characterizing the irreversibility of thermodynamic processes.
- Time-reversibility provides insights into the microscopic reversibility of physical systems.
Purpose of the Study:
- To formulate and investigate the entropy production rate for general jump diffusions.
- To explore the thermodynamic relations associated with entropy production in these processes.
- To establish the conditions for time-reversibility in stationary jump diffusions.
Main Methods:
- Formulation of the entropy production rate for jump diffusions.
- Derivation of the entropy production rate using relative entropy and Girsanov transform for stationary cases.
- Analysis of thermodynamic relations and detailed balance conditions.
Main Results:
- The entropy production rate for jump diffusions and its thermodynamic implications are established.
- A method to derive the entropy production rate for stationary jump diffusions using relative entropy is presented.
- Equivalence between time-reversibility, zero entropy production rate, detailed balance, and gradient structure is demonstrated for stationary jump diffusions.
Conclusions:
- The study provides a comprehensive framework for analyzing entropy production in jump diffusions.
- The findings offer a deeper understanding of the relationship between irreversibility and time-reversibility in stochastic processes.
- The established equivalences simplify the analysis of complex systems exhibiting Lévy dynamics.
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