scholarly journals Information Geometry of Non-Equilibrium Processes in a Bistable System with a Cubic Damping

Entropy ◽  
2017 ◽  
Vol 19 (6) ◽  
pp. 268 ◽  
Author(s):  
Rainer Hollerbach ◽  
Eun-jin Kim
Keyword(s):  
Information Geometry ◽  
Bistable System ◽  
Equilibrium Processes ◽  
Non Equilibrium

scholarly journals Information Geometry of Non-Equilibrium Processes in a Bistable System with a Cubic Damping

2017 ◽  
Author(s):  
Rainer Hollerbach ◽  
Eun-jin Kim
Keyword(s):  
Stochastic Systems ◽  
Entropy Change ◽  
Information Geometry ◽  
Rate Of Change ◽  
Bistable System ◽  
Equilibrium Processes ◽  
Probabilistic Description ◽  
The Difference ◽  
Comparison Of The Results ◽  
Non Equilibrium

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic systems and information geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time, and is called the information length. By using this concept, we investigate the information geometry of non-equilibrium processes involved in disorder-order transitions between the critical and subcritical states in a bistable system. Specifically, we compute time-dependent PDFs, information length, the rate of change in information length, entropy change and Fisher information in disorder-to-order and order-to-disorder transitions, and discuss similarities and disparities between the two transitions. In particular, we show that the total information length in order-to-disorder transition is much larger than that in disorder-to-order transition, and elucidate the link to the drastically different evolution of entropy in both transitions. We also provide the comparison of the results with those in the case of the transition between the subcritical and supercritical states and discuss implications for fitness.

scholarly journals Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1393
Author(s):  
Eun-jin Kim
Keyword(s):  
Geometric Theory ◽  
Information Geometry ◽  
Mean Value ◽  
Time Dependent ◽  
Entropy Production Rate ◽  
Time Varying ◽  
Research Fields ◽  
Equilibrium Processes ◽  
Over Time ◽  
Non Equilibrium

Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate Γ=dLdt and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, L is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control.

Multiplexed Laser Induced Fluorescence and Non-Equilibrium Processes in Arcjets.

1994 ◽  
Author(s):  
Dennis Keefer ◽  
Robert Rhodes ◽  
Trevor Moeller ◽  
David Burtner
Keyword(s):  
Laser Induced Fluorescence ◽  
Equilibrium Processes ◽  
Non Equilibrium

Additional Non Equilibrium Processes in the Dynamic Interaction between Flux Quanta and Defects

2006 ◽  
Author(s):  
S. Pace ◽  
G. Filatrella ◽  
G. Grimaldi ◽  
A. Nigro ◽  
M. G. Adesso
Keyword(s):  
Dynamic Interaction ◽  
Equilibrium Processes ◽  
Non Equilibrium

Self-Organisation of the Heat Resistant Steel Structure Following Dynamic Non-Equilibrium Processes

2015 ◽  
Vol 220-221 ◽  
pp. 917-921 ◽  
Author(s):  
Mykola Chausov ◽  
Pavlo Maruschak ◽  
Olegas Prentkovskis ◽  
Andriy Pylypenko ◽  
Valentyn Berezin ◽  
...  
Keyword(s):  
Dissipative Structure ◽  
Steel Structure ◽  
Image Correlation ◽  
Experimental Methodology ◽  
Resistant Steel ◽  
Heat Resistant Steel ◽  
Heat Resistant ◽  
Equilibrium Processes ◽  
Equilibrium Process ◽  
Non Equilibrium

Using an original experimental methodology and software for contactless investigation into strains applying the method of digital image correlation, conditions for DNP realization in the test setup with pre-set rigidity have been found. Strain velocities have been determined to be equal to 2...10 s–1 in the processes of forming and developing a dissipative structure of heat resistant steel under the DNP (dynamic non-equilibrium process).

scholarly journals Radicals and Non-Equilibrium Processes in Low-Temperature Plasmas

2007 ◽  
Vol 86 ◽  
pp. 011001 ◽  
Author(s):  
Zoran Petrović ◽  
Nigel Mason ◽  
Satoshi Hamaguchi ◽  
Marija Radmilović-Radjenović
Keyword(s):  
Low Temperature ◽  
Equilibrium Processes ◽  
Low Temperature Plasmas ◽  
Non Equilibrium

scholarly journals Photophysics of a copper phenanthroline elucidated by trajectory and wavepacket-based quantum dynamics: a synergetic approach

2017 ◽  
Vol 19 (30) ◽  
pp. 19590-19600 ◽  
Author(s):  
G. Capano ◽  
T. J. Penfold ◽  
M. Chergui ◽  
I. Tavernelli
Keyword(s):  
Molecular Dynamics ◽  
Excited State ◽  
Excited States ◽  
Ground State ◽  
Quantum Dynamics ◽  
Equilibrium Processes ◽  
Valuable Method ◽  
Non Equilibrium

On-the-fly excited state molecular dynamics is a valuable method for studying non-equilibrium processes in excited states and is beginning to emerge as a mature approach much like its ground state counterparts.

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