On the Nonequilibrium Entropy of Large and Small Systems

Sheldon Goldstein, David A. Huse, Joel L. Lebowitz, Pablo Sartori

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up these systems. A key element in this derivation is the large number of microscopic degrees of freedom of macroscopic systems. Therefore, the extension of thermodynamic concepts, such as entropy, to small (nano) systems raises many questions. Here we shall reexamine various definitions of entropy for nonequilibrium systems, large and small. These include thermodynamic (hydrodynamic), Boltzmann, and Gibbs-Shannon entropies. We shall argue that, despite its common use, the last is not an appropriate physical entropy for such systems, either isolated or in contact with thermal reservoirs: Physical entropies should depend on the microstate of the system, not on a subjective probability distribution. To square this point of view with experimental results of Bechhoefer we shall argue that the Gibbs-Shannon entropy of a nano particle in a thermal fluid should be interpreted as the Boltzmann entropy of a dilute gas of Brownian particles in the fluid.

Original languageEnglish (US)
Title of host publicationStochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017
EditorsGiambattista Giacomin, Stefano Olla, Ellen Saada, Herbert Spohn, Gabriel Stoltz, Gabriel Stoltz
PublisherSpringer New York LLC
Number of pages16
ISBN (Print)9783030150952
StatePublished - 2019
EventInternational workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017 - Paris, France
Duration: Jun 12 2017Jun 16 2017

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


ConferenceInternational workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Nonequilibrium thermodynamics
  • Statistical mechanics


Dive into the research topics of 'On the Nonequilibrium Entropy of Large and Small Systems'. Together they form a unique fingerprint.

Cite this