TY - JOUR
T1 - Thermodynamic Langevin equations
AU - Porporato, Amilcare
AU - Calabrese, Salvatore
AU - Rondoni, Lamberto
N1 - Publisher Copyright: © 2024 American Physical Society.
PY - 2024/11
Y1 - 2024/11
N2 - The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. Differently from the so-called stochastic thermodynamics, which starts from stochastic versions of the first and second law of thermodynamics and associates thermodynamic quantities to microscopic variables, here we consider stochastic variability directly in the macroscopic variables. By recognizing the potential structure of the Gibbs ensembles, when expressed as a function of the potential entropy generation, we obtain exact nonlinear thermodynamic Langevin equations (TLEs) for macroscopic variables, with drift expressed in terms of entropic forces. The analysis of the canonical ensemble for an ideal monoatomic gas and the related TLEs show that introducing currents leads to nonequilibrium heat transfer conditions with interesting bounds on entropy production but with no obvious thermodynamic limit. For a colloidal particle under constant force, the TLEs for macroscopic variables are different from those for the microscopic position, typically used in stochastic thermodynamics; while TLEs are consistent with the fundamental equation obtained from the Hamiltonian, stochastic thermodynamics requires isothermal conditions and entropy proportional to position.
AB - The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. Differently from the so-called stochastic thermodynamics, which starts from stochastic versions of the first and second law of thermodynamics and associates thermodynamic quantities to microscopic variables, here we consider stochastic variability directly in the macroscopic variables. By recognizing the potential structure of the Gibbs ensembles, when expressed as a function of the potential entropy generation, we obtain exact nonlinear thermodynamic Langevin equations (TLEs) for macroscopic variables, with drift expressed in terms of entropic forces. The analysis of the canonical ensemble for an ideal monoatomic gas and the related TLEs show that introducing currents leads to nonequilibrium heat transfer conditions with interesting bounds on entropy production but with no obvious thermodynamic limit. For a colloidal particle under constant force, the TLEs for macroscopic variables are different from those for the microscopic position, typically used in stochastic thermodynamics; while TLEs are consistent with the fundamental equation obtained from the Hamiltonian, stochastic thermodynamics requires isothermal conditions and entropy proportional to position.
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U2 - 10.1103/PhysRevE.110.054136
DO - 10.1103/PhysRevE.110.054136
M3 - Article
C2 - 39690693
SN - 2470-0045
VL - 110
JO - Physical Review E
JF - Physical Review E
IS - 5
M1 - 054136
ER -