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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.

The Entropy as a State Function

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...

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...

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 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...

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Updated: Jun 21, 2026

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

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

Published on: December 4, 2017

Longest excursion of stochastic processes in nonequilibrium systems.

Claude Godrèche¹, Satya N Majumdar, Grégory Schehr

¹Institut de Physique Théorique, IPhT, CEA Saclay, and URA 2306, 91191 Gif-sur-Yvette Cedex, France.

Physical Review Letters

|August 8, 2009

Summary

We analyzed the longest intervals between zeros in nonequilibrium systems. Smooth processes show linear growth, while nonsmooth processes exhibit linear or sublinear growth depending on a persistence exponent.

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Area of Science:

Statistical Physics
Non-equilibrium Dynamics
Stochastic Processes

Background:

Stochastic processes are fundamental to modeling complex systems.
Understanding the behavior of excursions (intervals between zeros) is crucial in nonequilibrium systems.
The temporal growth of the longest excursion has not been fully characterized across different process types.

Purpose of the Study:

To investigate the temporal growth of the longest excursion (l_max(t)) in various nonequilibrium stochastic processes.
To determine universal scaling behaviors and identify novel quantities governing this growth.
To differentiate growth patterns based on process smoothness and persistence properties.

Main Methods:

Exact analytical calculations for renewal and multiplicative processes.
Numerical simulations for systems like the Ising model (coarsening dynamics) and diffusion equations with random initial conditions.
Analysis of excursion intervals between consecutive zeros of stochastic processes.

Main Results:

For smooth processes, a universal linear growth l_max(t) ~ Q_infinity * t is observed, with Q_infinity being a model-dependent amplitude.
For nonsmooth processes with a persistence exponent theta, linear growth (l_max(t) ~ t) occurs if theta < theta_c.
For nonsmooth processes with theta > theta_c, sublinear growth l_max(t) ~ t^(1-psi) is found, where psi is a novel exponent.

Conclusions:

The study reveals distinct universal growth behaviors for the longest excursions in smooth versus nonsmooth nonequilibrium processes.
Novel quantities, Q_infinity and psi, characterize the amplitudes and scaling exponents of these growth dynamics.
The findings provide a comprehensive understanding of excursion dynamics across diverse physical systems.