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Fluctuation theorems from Bayesian retrodiction.

Francesco Buscemi¹, Valerio Scarani^2,3

¹Graduate School of Informatics, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan.

Physical Review. E

|June 17, 2021

Summary

This summary is machine-generated.

Bayesian retrodiction naturally defines the reverse process in statistical mechanics for both classical and quantum systems. This approach unifies and broadens fluctuation theorems, enhancing our understanding of irreversibility.

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Area of Science:

Statistical Mechanics
Quantum Mechanics
Bayesian Inference

Background:

Quantitative studies of irreversibility often grapple with defining the reverse process, especially in quantum systems.
Existing fluctuation theorems like Jarzynski's equality and Crooks' theorem have faced definitional challenges for reverse processes.

Purpose of the Study:

To demonstrate that Bayesian retrodiction provides a natural and unified framework for defining the reverse process in statistical mechanics.
To show the consistency of established fluctuation theorems with retrodictive arguments.
To generalize fluctuation relations by constructing the reverse process using logical inference.

Main Methods:

Applying Bayesian retrodiction to define reverse channels in classical and quantum theories.
Reinterpreting and validating paradigmatic results (Jarzynski's equality, Crooks' theorem, Tasaki's theorem) through a retrodictive lens.
Justifying corrections for non-equilibrium and open quantum systems as consequences of Bayesian retrodiction.

Main Results:

The reverse channel in statistical mechanics, both classical and quantum, arises naturally from Bayesian retrodiction.
Key fluctuation theorems are shown to be consistent with this retrodictive framework.
Corrections for non-equilibrium and open quantum systems are explained as remnants of Bayesian retrodiction.

Conclusions:

Bayesian retrodiction offers a unified and logically consistent method for defining reverse processes in statistical mechanics.
This approach broadens the scope and applicability of fluctuation relations.
The findings provide a more robust theoretical foundation for studying irreversibility in physical systems.