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Third Law of Thermodynamics

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

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

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.
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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

Entropy and the Second Law of Thermodynamics

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...

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Updated: Jan 13, 2026

DNA-Tethered RNA Polymerase for Programmable In vitro Transcription and Molecular Computation

DNA-Tethered RNA Polymerase for Programmable In vitro Transcription and Molecular Computation

Published on: December 29, 2021

Molecular computation at equilibrium via programmable entropy.

Boya Wang¹, Cameron Chalk¹, David Doty²

¹Electrical and Computer Engineering, University of Texas at Austin, Austin, TX 78712, USA.

Science Advances

|January 9, 2026

Summary

This summary is machine-generated.

This study introduces a new method for molecular information processing using DNA nanotechnology. It programs the thermodynamic equilibrium state, enabling complex molecular behaviors through entropic forces.

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Area of Science:

Molecular engineering
Biotechnology
Computational biology

Background:

Synthetic molecular information processing traditionally relies on programming kinetic pathways for molecular interactions.
This kinetic programming can lead to errors when thermodynamic forces oppose the intended sequence of molecular events.

Purpose of the Study:

To demonstrate an alternative paradigm in dynamic DNA nanotechnology for molecular information processing.
To program the thermodynamic equilibrium state directly, leveraging entropic driving forces for computation.
To simplify molecular programming and enhance reliability by aligning with natural thermodynamic principles.

Main Methods:

Utilizing dynamic DNA nanotechnology to directly program thermodynamic equilibrium states.
Employing entropic driving forces as the basis for molecular computation.
Developing applications based on declarative programming principles for molecular systems.

Main Results:

Demonstrated reversible signal propagation with fan-in and fan-out capabilities.
Achieved algorithmic self-assembly capable of performing Boolean logic operations.
Enabled the synthesis of molecular chains (concatemers) with programmable lengths.
Illustrated the practical application of thermodynamic computation in molecular engineering.

Conclusions:

Thermodynamic computation offers a robust and simplified approach to molecular information processing compared to kinetic programming.
This approach has broad applicability in areas such as signal processing, logic operations, and molecular synthesis.
The findings expand the possibilities for engineering complex molecular behaviors and understanding the interplay between thermodynamics and kinetics in molecular systems.