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Entropy Change in Reversible Processes01:10

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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.
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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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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α-divergence improves the entropy production estimation via machine learning.

Euijoon Kwon1, Yongjoo Baek1

  • 1Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul 08826, Republic of Korea.

Physical Review. E
|February 17, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a new machine learning method, α-NEEP (Neural Estimator for Entropy Production), for accurately estimating stochastic entropy production. The novel approach uses α-divergence loss functions, offering improved robustness over existing methods, especially under challenging conditions.

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Area of Science:

  • Statistical mechanics
  • Machine learning
  • Non-equilibrium thermodynamics

Background:

  • Accurate estimation of stochastic entropy production (EP) from trajectory data is crucial for understanding non-equilibrium systems.
  • Existing machine learning methods often rely on Kullback-Leibler divergence, which can be sensitive to strong non-equilibrium driving or slow dynamics.

Purpose of the Study:

  • To introduce and validate a new class of loss functions for machine learning-based EP estimation.
  • To demonstrate the enhanced robustness of the proposed method compared to existing approaches.

Main Methods:

  • Development of the α-NEEP (Neural Estimator for Entropy Production) using a variational representation of the α-divergence.
  • Testing the α-NEEP with a range of α values, particularly between -1 and 0.
  • Analysis of an exactly solvable EP estimation problem to understand the loss function landscape and stochastic properties.

Main Results:

  • The α-NEEP, utilizing α-divergence loss functions, shows significantly improved robustness against strong non-equilibrium driving and slow dynamics.
  • Performance is superior to the standard Kullback-Leibler divergence (α=0) based method.
  • Optimal results are frequently achieved with α=-0.5.

Conclusions:

  • The α-NEEP provides a more robust and accurate method for estimating stochastic entropy production.
  • The choice of α in the α-divergence offers a tunable parameter for optimizing performance in various non-equilibrium scenarios.