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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.

Entropy

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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

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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.
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Consider an infinitesimal step in the expansion, which...

Entropy and the Second Law of Thermodynamics

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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...

Gibbs Free Energy

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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...

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Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

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Entropy Governed by the Absorbing State of Directed Percolation.

Kenji Harada¹, Naoki Kawashima²

¹Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.

Physical Review Letters

|September 17, 2019

Summary

This summary is machine-generated.

We explored directed percolation, finding universal Rényi entropy relaxation at the absorbing transition. A new singularity with cusped Rényi and entanglement entropy was discovered in the active phase.

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Area of Science:

Physics
Statistical Mechanics
Complex Systems

Background:

Directed percolation is a key model for nonequilibrium phase transitions.
Understanding the absorbing state is crucial for characterizing these transitions.
Information dynamics in such systems remain an active area of research.

Purpose of the Study:

To investigate the informational aspects of (1+1)-dimensional directed percolation.
To analyze the time evolution of state probability distribution and associated entropies.
To uncover novel phenomena related to the absorbing state and phase transitions.

Main Methods:

Utilized a tensor network scheme for numerical calculations.
Computed the time evolution of the state probability distribution.
Analyzed Rényi and entanglement entropy dynamics.

Main Results:

Observed universal relaxation of Rényi entropy at the absorbing phase transition.
Identified a new singularity in the active phase with a cusp in second-order Rényi entropy.
Detected singular behavior in entanglement entropy, vanishing below and finite above the new singular point.
Confirmed the absorbing state's role in these phenomena.

Conclusions:

The absorbing state, even when rare, drives critical phenomena in directed percolation.
A unified understanding of Rényi entropy evolution across critical and active phases is provided.
The study reveals new insights into nonequilibrium phase transitions and information dynamics.