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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 and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...

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

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...

Entropy Changes Accompanying Specific Processes

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...

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Updated: Mar 3, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Entropy Production in Non-Gaussian Active Matter: A Unified Fluctuation Theorem and Deep Learning Framework.

Yuanfei Huang^1,2, Chengyu Liu³, Bing Miao⁴

¹Asia Pacific Center for Theoretical Physics, Pohang-si, Gyeongsangbuk-do, 37673, Republic of Korea.

Physical Review Letters

|March 1, 2026

Summary

We developed a framework to calculate entropy production in active matter systems with non-Gaussian fluctuations. This method provides a unified approach and computational tools for studying complex nonequilibrium behaviors.

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Area of Science:

Physics
Statistical Mechanics
Soft Matter

Background:

Active matter systems exhibit complex nonequilibrium dynamics driven by internal energy consumption.
Understanding entropy production is crucial for characterizing these systems, but non-Gaussian fluctuations pose challenges.
Existing methods in stochastic thermodynamics often struggle with non-Gaussian active fluctuations.

Purpose of the Study:

To develop a general theoretical framework for deriving entropy production rates in active matter systems driven by non-Gaussian active fluctuations.
To establish fluctuation theorems and thermodynamic inequalities for these systems.
To introduce a novel deep-learning-based computational method for efficiently calculating entropy production.

Main Methods:

Utilized the probability-flow equivalence technique to derive an entropy production decomposition formula.
Demonstrated detailed and integral fluctuation theorems, including a generalized second law of thermodynamics.
Proposed a deep-learning methodology incorporating a Lévy score for efficient entropy production computation.

Main Results:

Derived a rigorous entropy production decomposition formula applicable to non-Gaussian active systems.
Established that the total entropy production satisfies detailed and integral fluctuation theorems.
Showcased the generalized second law of thermodynamics for active matter systems.
Validated the deep-learning approach on a Brownian particle in an active bath and an active polymer model.

Conclusions:

The presented framework offers a unified approach to analyze entropy production in active matter.
The developed computational tools enable efficient investigation of complex nonequilibrium phenomena.
The findings extend stochastic thermodynamics to systems with non-Gaussian active fluctuations.