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Related Concept Videos

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...
Entropy01:18

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...
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...
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...
Entropy and Solvation02:05

Entropy and Solvation

The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ ≥ 15); an...

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Related Experiment Videos

How hidden are hidden processes? A primer on crypticity and entropy convergence.

John R Mahoney1, Christopher J Ellison, Ryan G James

  • 1Physics Department, University of California at Merced, 5200 North Lake Road, Merced, California 95343, USA. jmahoney3@ucmerced.edu

Chaos (Woodbury, N.Y.)
|October 7, 2011
PubMed
Summary

We introduce crypticity, a measure of process hiddenness, using computational mechanics. This work establishes crypticity and cryptic order as key physical quantities for understanding complex systems.

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Area of Science:

  • Statistical physics
  • Information theory
  • Dynamical systems

Background:

  • Stationary processes possess hidden states not fully captured by observations.
  • Computational mechanics provides tools to analyze these hidden states using causal states.
  • Crypticity quantifies the information difference between hidden and observed states.

Purpose of the Study:

  • To establish crypticity and cryptic order as physically meaningful quantities.
  • To provide a geometric interpretation of previous results on entropy convergence.
  • To develop a classification scheme for stationary processes based on their hiddenness.

Main Methods:

  • Utilizing the causal states framework from computational mechanics.
  • Recasting entropy convergence results in a geometric setting.
  • Analyzing spin chains and developing a classification scheme for stationary processes.

Main Results:

  • Crypticity is linked to observer synchronization with a process.
  • Block-causal-state entropy is shown to be a convex function of block length.
  • A classification of stationary processes based on cryptic and Markov orders is presented.

Conclusions:

  • Crypticity and cryptic order are natural and pervasive quantities.
  • The geometric approach offers new insights into information dynamics.
  • This work lays the foundation for applications in network and extended dynamical systems.