TY - GEN
T1 - On the Nonequilibrium Entropy of Large and Small Systems
AU - Goldstein, Sheldon
AU - Huse, David A.
AU - Lebowitz, Joel L.
AU - Sartori, Pablo
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Nonequilibrium thermodynamics
KW - Statistical mechanics
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U2 - 10.1007/978-3-030-15096-9_22
DO - 10.1007/978-3-030-15096-9_22
M3 - Conference contribution
AN - SCOPUS:85069531104
SN - 9783030150952
T3 - Springer Proceedings in Mathematics and Statistics
SP - 581
EP - 596
BT - Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017
A2 - Giacomin, Giambattista
A2 - Olla, Stefano
A2 - Saada, Ellen
A2 - Spohn, Herbert
A2 - Stoltz, Gabriel
A2 - Stoltz, Gabriel
PB - Springer New York LLC
T2 - International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017
Y2 - 12 June 2017 through 16 June 2017
ER -