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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...

Third Law of Thermodynamics

Third Law of Thermodynamics

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

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...

Second Law of Thermodynamics

Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

Second Law of Thermodynamics

Second Law of Thermodynamics

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...

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Steady-state, Pre-steady-state, and Single-turnover Kinetic Measurement for DNA Glycosylase Activity

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Steady-state entropy: A proposal based on thermodynamic integration.

Leonardo Ferreira Calazans¹, Ronald Dickman¹

¹Departamento de Física and National Institute of Science and Technology for Complex Systems, ICEx, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil.

Physical Review. E

|April 20, 2019

Summary

This summary is machine-generated.

Defining thermodynamic entropy out of equilibrium remains challenging. This study shows that while a constructed entropy (S_th) matches equilibrium expectations, it differs from Shannon entropy (S_S) in nonequilibrium steady states, questioning its role as a state function.

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Area of Science:

Statistical Mechanics
Non-equilibrium Thermodynamics
Complex Systems

Background:

Defining entropy for systems out of equilibrium is a significant challenge in statistical mechanics.
Previous work established definitions for temperature and chemical potential in nonequilibrium steady states using reservoir coexistence.
These definitions satisfy the zeroth law, paving the way for steady-state thermodynamics.

Purpose of the Study:

To investigate the validity and properties of a constructed steady-state entropy (S_th) in nonequilibrium systems.
To compare this constructed entropy with the Shannon entropy (S_S) in driven lattice models.
To determine if S_th is a state function and if S_S maximization governs nonequilibrium steady states.

Main Methods:

Direct calculation of stationary nonequilibrium probability distributions for specific lattice models (Katz-Lebowitz-Spohn driven lattice gas, two-temperature Ising model).
Evaluation of both Shannon entropy (S_S) and a thermodynamically constructed entropy (S_th) using calculated distributions.
Analysis of the dependence of S_th on thermodynamic paths to test its state function property.

Main Results:

The constructed entropy (S_th) and Shannon entropy (S_S) are identical in equilibrium but differ in nonequilibrium steady states.
The difference between S_S and S_th scales quadratically with the driving force (D) for small drives (|S_S - S_th| ∝ D^2).
S_th was found not to be a state function, as its changes depend on the integration path.

Conclusions:

The inequivalence of S_S and S_th suggests that maximizing Shannon entropy does not determine nonequilibrium steady states.
Derivatives of S_S do not predict coexistence, challenging its predictive power in nonequilibrium thermodynamics.
The findings cast doubt on the existence of a general state function that serves as a thermodynamic entropy for all nonequilibrium steady states.