scholarly journals Reparametrizations and metric structures in thermodynamic phase space

2021 ◽  
Vol 563 ◽  
pp. 125464
Author(s):  
V. Pineda-Reyes ◽  
L.F. Escamilla-Herrera ◽  
C. Gruber ◽  
F. Nettel ◽  
H. Quevedo
Keyword(s):  
Phase Space ◽  
Metric Structures ◽  
Thermodynamic Phase

scholarly journals Metric Thermodynamic Phase Space and Stability Problems

2016 ◽  
Vol 49 (24) ◽  
pp. 52-57
Author(s):  
Nicolas Hudon ◽  
Martin Guay ◽  
Denis Dochain
Keyword(s):  
Phase Space ◽  
Stability Problems ◽  
Thermodynamic Phase

scholarly journals The Entropic Dynamics Approach to Quantum Mechanics

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 943 ◽  
Author(s):  
Ariel Caticha
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Hilbert Spaces ◽  
Symplectic Structure ◽  
Superposition Principle ◽  
Information Geometry ◽  
Wave Functions ◽  
Hamiltonian Flows ◽  
Metric Structures ◽  
Entropic Dynamics

Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures—which is a Hamilton-Killing flow in phase space—is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations.

scholarly journals Geometric Analysis of a System with Chemical Interactions

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1548
Author(s):  
Dmitry Gromov ◽  
Alexander Toikka
Keyword(s):  
Phase Space ◽  
Chemical Reactions ◽  
Geometric Analysis ◽  
Stability Conditions ◽  
Chemical Interactions ◽  
Thermodynamic Phase ◽  
Initial Results

In this paper, we present some initial results aimed at defining a framework for the analysis of thermodynamic systems with additional restrictions imposed on the intensive parameters. Specifically, for the case of chemical reactions, we considered the states of constant affinity that form isoffine submanifolds of the thermodynamic phase space. Wer discuss the problem of extending the previously obtained stability conditions to the considered class of systems.

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