We investigate the time evolution of the correlation functions of a nonequilibrium system when the size of the system becomes very large. At the initial time t = 0, the system is represented by an equilibrium grand canonical ensemble with a Hamiltonian consisting of a kinetic energy part, a pairwise interaction potential energy between the particles, and an external potential. At time t = 0 the external field is turned off and the system is permitted to evolve under its internal Hamiltonian alone. Using the ``time‐evolution theorem'' for a 1‐dimensional system with bounded finite‐range pair forces, we prove the existence of infinite‐volume time‐dependent correlation functions for such systems, limρΛ(t;q1,p1;⋯;qn,pn), as Λ→∞, where Λ is the size of the finite system. We also show that these infinite‐volume correlation functions satisfy the infinite BBGKY hierarchy in the sense of distributions.
Thermodynamic limit of time--dependent correlation functions for one--dimensional systems / Gallavotti, Giovanni; O., Lanford; J., Lebowitz. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 11:(1970), pp. 2898-2905. [10.1063/1.1665459]
Thermodynamic limit of time--dependent correlation functions for one--dimensional systems
GALLAVOTTI, Giovanni;
1970
Abstract
We investigate the time evolution of the correlation functions of a nonequilibrium system when the size of the system becomes very large. At the initial time t = 0, the system is represented by an equilibrium grand canonical ensemble with a Hamiltonian consisting of a kinetic energy part, a pairwise interaction potential energy between the particles, and an external potential. At time t = 0 the external field is turned off and the system is permitted to evolve under its internal Hamiltonian alone. Using the ``time‐evolution theorem'' for a 1‐dimensional system with bounded finite‐range pair forces, we prove the existence of infinite‐volume time‐dependent correlation functions for such systems, limρΛ(t;q1,p1;⋯;qn,pn), as Λ→∞, where Λ is the size of the finite system. We also show that these infinite‐volume correlation functions satisfy the infinite BBGKY hierarchy in the sense of distributions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.