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Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Gibbs Free Energy

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...

Gibbs Free Energy and Thermodynamic Favorability

Gibbs Free Energy and Thermodynamic Favorability

The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...

Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

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Entropic Dynamics on Gibbs Statistical Manifolds.

Pedro Pessoa¹, Felipe Xavier Costa¹, Ariel Caticha¹

¹Department of Physics, University at Albany (SUNY), Albany, NY 12222, USA.

Entropy (Basel, Switzerland)

|April 30, 2021

Summary

This summary is machine-generated.

Entropic dynamics derives physical laws from probabilistic inference. This study applies entropic methods to statistical manifolds, introducing an intrinsic, directional "entropic time" for systems.

Keywords:

canonical distributions entropic dynamics exponential family information geometry maximum entropy

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Area of Science:

Theoretical Physics
Statistical Mechanics
Information Geometry

Background:

Entropic dynamics offers a framework for deriving physical laws from probabilistic principles.
Previous successes include deriving quantum mechanics and quantum field theory.
The dynamics of a system can be viewed on a statistical manifold.

Purpose of the Study:

To develop entropic dynamics for systems described by probability distributions.
To investigate the role of statistical manifold geometry, specifically curvature, in entropic dynamics.
To explore an intrinsic, system-tailored notion of 'entropic time'.

Main Methods:

Utilizing information geometry to define a metric structure on the statistical manifold.
Focusing the dynamics on the statistical manifold of Gibbs (exponential family) distributions.
Developing a system-specific 'entropic time' as an intrinsic measure of temporal progression.

Main Results:

The dynamics unfold on a statistically manifold endowed with a natural metric structure.
The curvature of the statistical manifold significantly influences the dynamics.
An intrinsic, directional 'entropic time' emerges, driven by entropic considerations.

Conclusions:

Entropic dynamics can be effectively applied to systems described by probability distributions on statistical manifolds.
The geometric properties of these manifolds are crucial for understanding the resulting dynamics.
The concept of entropic time provides a natural arrow of time rooted in entropic principles.