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The information geometry of two-field functional integrals.

Eric Smith1,2,3,4

  • 1Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1-IE-1 Ookayama, Meguro-ku, Tokyo, 152-8550 Japan.

Information Geometry
|November 30, 2022
PubMed
Summary
This summary is machine-generated.

Two-field functional integrals (2FFI) reveal conserved quantities in stochastic processes, offering new insights into Wigner functions and overlap functions. This advances understanding of dissipative systems and quantum densities.

Keywords:
Doi-Peliti theoryFisher informationInformation geometryLiouville’s theoremdualityimportance sampling

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Information Geometry

Background:

  • Two-field functional integrals (2FFI) are key for analyzing dissipative processes like stochastic systems and quantum densities.
  • Conserved currents in these systems are not always apparent from kinematic properties alone.

Purpose of the Study:

  • To explore the information geometry of generating functions for classical stochastic processes using the Doi-Peliti 2FFI framework.
  • To identify and interpret quantities conserved along stationary trajectories within this framework.

Main Methods:

  • Developed the information geometry of generating functions for discrete-state classical stochastic processes.
  • Utilized the Doi-Peliti two-field functional integral (2FFI) formalism.
  • Investigated stationary trajectories and conserved quantities, including Wigner and overlap functions.

Main Results:

  • Identified two conserved quantities along stationary trajectories: a Wigner function and an overlap function.
  • The overlap function relates variations in distribution and large-deviation probabilities, expressed via the Fisher information metric.
  • Derived dual affine connections specific to Doi-Peliti theory, highlighting the roles of nominal distribution and likelihood ratio.

Conclusions:

  • The conserved Fisher information relates to sample volume changes under distribution and likelihood ratio deformations.
  • Dual flatness in coherent-state basis coordinates underscores the significance of coherent states in Doi-Peliti theory.
  • This work provides a deeper understanding of conserved quantities and geometric structures in dissipative systems.