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Related Concept Videos

Entropy Change in Reversible Processes01:10

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 Changes Accompanying Specific Processes01:21

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 results...
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
The Second Law of Thermodynamics01:14

The 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. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be put...
Gibbs Free Energy02:39

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...
Spontaneity02:21

Spontaneity

A spontaneous process is one that occurs naturally under certain conditions. A nonspontaneous process, on the other hand, will not take place unless it is “driven” by the continual input of energy from an external source. Processes have a natural tendency to occur in one direction under a given set of conditions. Water will naturally flow downhill (spontaneous process), but uphill flow (nonspontaneous process) requires outside intervention such as the use of a pump. Iron exposed to the earth’s...

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Related Experiment Video

Updated: May 18, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

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

Published on: December 4, 2017

Stochastic energetics for non-Gaussian processes.

Kiyoshi Kanazawa1, Takahiro Sagawa, Hisao Hayakawa

  • 1Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto, Japan.

Physical Review Letters
|September 26, 2012
PubMed
Summary

We developed a new stochastic integral to analyze the energy changes in classical systems subjected to non-Gaussian white noise. This method allows calculating heat from trajectory data, applicable to systems like Poisson-driven Langevin dynamics.

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Area of Science:

  • Statistical physics
  • Non-equilibrium thermodynamics
  • Stochastic processes

Background:

  • Classical stochastic systems are often modeled using Gaussian white noise.
  • Analyzing the energetics of systems driven by non-Gaussian noise presents significant challenges.
  • Understanding energy fluctuations (work and heat) is crucial in non-equilibrium statistical mechanics.

Purpose of the Study:

  • To introduce a novel stochastic integral for investigating the energetics of classical stochastic systems driven by non-Gaussian white noises.
  • To decompose the total energy difference into work and heat for individual trajectories.
  • To derive a practical formula for calculating heat from experimental dynamics data.

Main Methods:

  • Development of a new stochastic integral tailored for non-Gaussian noise.
  • Trajectory-based decomposition of energy changes into work and heat.
  • Application of the derived formalism to a Langevin system driven by Poisson noise.

Main Results:

  • A new theoretical framework for analyzing the energetics of stochastic systems with non-Gaussian driving forces.
  • A method to quantify heat production from observable dynamic trajectories.
  • Successful application and validation of the method on a specific non-Gaussian system (Poisson noise).

Conclusions:

  • The introduced stochastic integral provides a powerful tool for studying non-equilibrium energetics.
  • The derived formula enables experimental determination of heat in complex stochastic systems.
  • The findings advance the understanding of energy dissipation in systems beyond simple Gaussian noise models.