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Related Concept Videos

Calculation of First-Law Quantities II01:24

Calculation of First-Law Quantities II

The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...
Pressure and Volume in an Adiabatic Process01:27

Pressure and Volume in an Adiabatic Process

Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is,
Adiabatic Processes for an Ideal Gas01:18

Adiabatic Processes for an Ideal Gas

When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
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 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...
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...

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Related Experiment Video

Updated: May 28, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

A First-Principles Thermodynamic Uncertainty Relation for Shortcuts to Adiabaticity.

Guillermo Ezequiel Perna1,2, Federico Centrone3, Esteban Calzetta1,2

  • 1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Ciudad de Buenos Aires CP 1428, Argentina.

Entropy (Basel, Switzerland)
|May 26, 2026
PubMed
Summary
This summary is machine-generated.

Implementing quantum time-dependent protocols faces limitations when using quantum clocks. A new study reveals a thermodynamic uncertainty tradeoff linking precision to purity loss, crucial for quantum control precision.

Keywords:
quantum clocksshortcuts to adiabaticitythermodynamic uncertainty relations

Related Experiment Videos

Last Updated: May 28, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Area of Science:

  • Quantum mechanics
  • Quantum information science
  • Quantum thermodynamics

Background:

  • Time-dependent Hamiltonian protocols are essential for controlling quantum systems.
  • Traditionally, 'time' is an external classical parameter, but using a quantum clock introduces fundamental limitations.
  • Shortcuts-to-adiabaticity (STA) offer faster control but are sensitive to implementation details.

Purpose of the Study:

  • To investigate the fundamental limitations of implementing time-dependent Hamiltonian protocols using a quantum clock.
  • To analyze the impact of a minimal clock degree of freedom on the system's dynamics and achievable precision.
  • To establish a quantitative relationship between control precision and state purity loss.

Main Methods:

  • Studied a parametric harmonic oscillator controlled via an STA schedule.
  • Coupled the oscillator to a minimal quantum clock degree of freedom.
  • Traced out the clock to derive the effective reduced dynamics.
  • Computed energetic deviation, fluctuations, fidelity, and purity loss in a noise-dominated regime for vacuum and coherent states.

Main Results:

  • Tracing out the quantum clock leads to a reduced dynamics described by a mixture of unitary Gaussian trajectories.
  • In the noise-dominated regime, energetic deviation, fidelity, and purity loss were quantified.
  • A thermodynamic-uncertainty-type tradeoff was identified, connecting precision to irreducible purity loss.

Conclusions:

  • The precision of quantum control protocols using quantum clocks is fundamentally limited by the clock's precision and protocol sensitivity.
  • This limitation manifests as an irreducible loss of quantum state purity.
  • The findings are crucial for understanding and optimizing quantum control strategies in realistic noisy quantum systems.