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Maxwell's Thermodynamic Relations

Maxwell's Thermodynamic Relations

Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...

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Updated: May 11, 2026

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

Published on: January 19, 2018

Probing Maxwell's demon with a nanoscale thermometer.

Justin P Bergfield¹, Shauna M Story, Robert C Stafford

¹Department of Chemistry, Northwestern University, 1818 Hinman Avenue, Evanston, Illinois 60208, United States. justin.bergfield@northwestern.edu

|May 9, 2013

Summary

A quantum electron thermometer reveals quantum oscillations in molecular temperatures due to a Maxwell

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Last Updated: May 11, 2026

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

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Scanning-probe Single-electron Capacitance Spectroscopy

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Published on: July 30, 2013

Area of Science:

Quantum physics
Molecular dynamics
Nanoscale thermodynamics

Background:

A precise definition of a quantum electron thermometer (QET) is established.
A realistic model for a scanning thermal microscope (STM) with atomic resolution is developed, incorporating environmental thermal coupling.

Purpose of the Study:

To investigate quantum phenomena in molecular temperature gradients.
To explore the link between quantum mechanics and classical heat conduction laws.

Main Methods:

Development of a QET model.
Simulation of a scanning thermal microscope with atomic resolution.
Analysis of temperature oscillations in conjugated molecules.

Main Results:

Quantum oscillations observed in atomic orbital/bond temperatures within a molecule exhibiting a temperature gradient.
Origin of oscillations traced to a single-molecule Maxwell's demon.
Oscillations explained by covalence rules in π-electron systems.

Conclusions:

Quantum effects, like Maxwell's demon, manifest at the single-molecule level.
Macroscopic Fourier's law of heat conduction emerges from coarse-graining quantum phenomena.