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Entropy

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

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...

Second Law of Thermodynamics

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. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

The Second Law of Thermodynamics

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...

Entropy Change in Reversible Processes

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 within the Cell

Entropy within the Cell

A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that...

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Related Experiment Video

Updated: Jan 9, 2026

Induction of an Isoelectric Brain State to Investigate the Impact of Endogenous Synaptic Activity on Neuronal Excitability In Vivo

Induction of an Isoelectric Brain State to Investigate the Impact of Endogenous Synaptic Activity on Neuronal Excitability In Vivo

Published on: March 31, 2016

State-space kinetic Ising model reveals task-dependent entropy flow in sparsely active nonequilibrium neuronal

Ken Ishihara^1,2, Hideaki Shimazaki^3,4

¹Graduate School of Life Science, Hokkaido University, Sapporo, Japan. ishihara.ken.n7@elms.hokudai.ac.jp.

Nature Communications

|December 9, 2025

Summary

We developed a new model to measure time asymmetry in neuronal activity, revealing how brain organization relates to computation. Higher-performing mice showed more efficient neural communication during tasks.

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Last Updated: Jan 9, 2026

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Published on: March 31, 2016

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Published on: October 17, 2025

Area of Science:

Neuroscience
Computational Neuroscience
Statistical Physics

Background:

Neuronal ensemble activity displays nonequilibrium characteristics, crucial for maintaining organization.
Assessing time asymmetry in spiking neural activity is challenging, especially with nonstationary dynamics.

Purpose of the Study:

To develop a novel state-space kinetic Ising model for analyzing nonstationary and nonequilibrium neural dynamics.
To estimate time-varying entropy flow and causal couplings in neuronal activity.
To link thermodynamic principles of neural computation to behavioral performance.

Main Methods:

Developed a state-space kinetic Ising model incorporating a mean-field method for entropy flow estimation.
Applied the model to mouse visual cortex data, analyzing neuronal firing rates and coupling strengths.
Quantified time-varying entropy flow and causal couplings during different behavioral states.

Main Results:

Identified greater variability in causal couplings in the mouse visual cortex during task engagement.
Observed reduced neuronal activity and increased sparsity during task performance.
Found increased coupling-related entropy flow per spike in higher-performing mice during task engagement.

Conclusions:

The state-space kinetic Ising model effectively captures asymmetric causal dynamics in nonstationary neural systems.
Increased entropy flow per spike correlates with more efficient neural computation and better behavioral performance.
This work provides a thermodynamic framework for understanding neural computation and its link to behavior.