TY - JOUR
T1 - On the fluctuation-dissipation theorem for convective processes
AU - McKane, Alan J.
AU - Vázquez, Federico
AU - Olivares-Robles, Miguel A.
N1 - Funding Information:
We wish to thank Y. Oono and M. López de Haro for useful discussions. AJM wishes to thank the Department of Physics at the Universidad Autón-oma del Estado de Morelos for hospitality while this work was carried out. Financial support from CONACYT-México under project number 40454 and from PROMEP-México is gratefully acknowledged.
PY - 2007/2/20
Y1 - 2007/2/20
N2 - When making the connection between the thermodynamics of irreversible processes and the theory of stochastic processes through the uctuation-dissipation theorem, it is necessary to invoke a postulate of the Einstein-Boltzmann type. For convective processes hydrodynamic uctuations must be included; the velocity is a dynamical variable and although the entropy cannot depend directly on the velocity, δ2S will depend on velocity variations. Some authors do not include velocity variations in δ2S, and so have to introduce a non-thermodynamic function which replaces the entropy and does depend on the velocity. At rst sight, it seems that the introduction of such a function requires a generalisation of the Einstein-Boltzmann relation to be invoked. We review the reason why it is not necessary to introduce such a function, and therefore why there is no need to generalise the Einstein-Boltzmann relation in this way. We then obtain the uctuation-dissipation theorem, which shows some differences as compared with the non-convective case. We also show that δ2S is a Liapunov function when it includes velocity uctuations.
AB - When making the connection between the thermodynamics of irreversible processes and the theory of stochastic processes through the uctuation-dissipation theorem, it is necessary to invoke a postulate of the Einstein-Boltzmann type. For convective processes hydrodynamic uctuations must be included; the velocity is a dynamical variable and although the entropy cannot depend directly on the velocity, δ2S will depend on velocity variations. Some authors do not include velocity variations in δ2S, and so have to introduce a non-thermodynamic function which replaces the entropy and does depend on the velocity. At rst sight, it seems that the introduction of such a function requires a generalisation of the Einstein-Boltzmann relation to be invoked. We review the reason why it is not necessary to introduce such a function, and therefore why there is no need to generalise the Einstein-Boltzmann relation in this way. We then obtain the uctuation-dissipation theorem, which shows some differences as compared with the non-convective case. We also show that δ2S is a Liapunov function when it includes velocity uctuations.
UR - http://www.scopus.com/inward/record.url?scp=33847285933&partnerID=8YFLogxK
U2 - 10.1515/JNETDY.2007.002
DO - 10.1515/JNETDY.2007.002
M3 - Artículo
SN - 0340-0204
VL - 32
SP - 29
EP - 40
JO - Journal of Non-Equilibrium Thermodynamics
JF - Journal of Non-Equilibrium Thermodynamics
IS - 1
ER -