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Stochastic functionals and fluctuation theorem for multikangaroo processes.

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Summary
This summary is machine-generated.

We introduce multikangaroo Markov processes for analyzing stochastic systems. This method analytically calculates large deviation properties and applies to stochastic thermodynamics and zero-crossing statistics.

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Area of Science:

  • Statistical physics
  • Stochastic processes
  • Non-equilibrium thermodynamics

Background:

  • Markov processes are fundamental in modeling systems with memoryless transitions.
  • Stochastic functionals are crucial for understanding complex system dynamics.
  • Large deviation theory provides insights into rare events in stochastic systems.

Purpose of the Study:

  • Introduce multikangaroo Markov processes.
  • Develop a general procedure for evaluating stochastic functionals.
  • Analyze large deviation properties and applications in thermodynamics and statistics.

Main Methods:

  • Definition and analysis of multikangaroo Markov processes.
  • Analytical calculation of large deviation properties.
  • Application to zero-crossing statistics and stochastic thermodynamics.

Main Results:

  • A general procedure for evaluating a specific type of stochastic functional.
  • Analytical results for large deviation properties.
  • Derivation of the fluctuation theorem and large deviation properties for stochastic entropy production.

Conclusions:

  • Multikangaroo Markov processes offer a novel framework for stochastic analysis.
  • The developed methods provide exact results for large deviation properties.
  • The findings have direct implications for understanding non-equilibrium systems, particularly in solid-state devices.