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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.
The Entropy as a State Function01:14

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...
Entropy and the Second Law of Thermodynamics01:26

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 and the Second Law of Thermodynamics01:20

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 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...
Entropy02:39

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...

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Large deviations of ergodic counting processes: a statistical mechanics approach.

Adrián A Budini1

  • 1Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche, Avenida E Bustillo Km 9.5, 8400 Bariloche, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

Large-deviation methods characterize counting processes using a thermodynamic framework. A statistical mechanics approach reveals an auxiliary process offering a new measurement interpretation for fluctuations.

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Area of Science:

  • Statistical Mechanics
  • Information Theory
  • Stochastic Processes

Background:

  • Large-deviation methods analyze ergodic counting processes using a thermodynamic framework.
  • Free energy functions characterize asymptotic statistical properties of fluctuations.

Purpose of the Study:

  • To explore the thermodynamic formalism of large deviations via a statistical mechanics approach.
  • To introduce an auxiliary counting process for interpreting thermodynamic potentials.

Main Methods:

  • Employing a statistical mechanics approach with an auxiliary counting process.
  • Maximizing an entropy function associated with the thermodynamic potential.
  • Applying a conditional measurement scheme to original counting processes.

Main Results:

  • Demonstrated an alternative measurement interpretation of the thermodynamic approach.
  • Derived general results for renewal counting processes.
  • Showcased scale invariance, shift closure, and intermittence phenomena.

Conclusions:

  • The statistical mechanics of renewal processes are controlled by rescaled waiting time distributions.
  • Similar findings extend to nonrenewal processes with stochastic waiting times.
  • The study provides a novel perspective on thermodynamic interpretations in counting processes.