Heat fluctuations in the two-time CPT, Universit de Toulon - PowerPoint PPT Presentation

Heat fluctuations in the two-time measurement framework and ultraviolet regularity Annalisa Panati, Heat fluctuations in the two-time CPT, Université de Toulon measurement framework and ultraviolet Plan Context: quantum regularity statistical mechanics joint work with T.Benoist, (Y. Pautrat) and R. Raquépas Fluctuation relations Two-time measurment statistics Conservation laws Annalisa Panati, Heat fluctuations: theorems and CPT, Université de Toulon results Bounded perturbations Conclusions

Heat fluctuations in the two-time measurement framework and ultraviolet regularity Context: quantum statistical mechanics Annalisa Panati, CPT, Université Fluctuation relations de Toulon Plan Context: quantum statistical Two-time measurment statistics mechanics Conservation laws Fluctuation relations Two-time measurment statistics Conservation laws Heat fluctuations: theorems and results Heat fluctuations: theorems and Bounded perturbations results Bounded perturbations Conclusions Conclusions

Heat fluctuations Context: quantum statistical mechanics in the two-time measurement framework and Fluctuation relations ultraviolet regularity Annalisa Panati, CPT, Université de Toulon Plan Context: quantum statistical mechanics Fluctuation relations Two-time measurment statistics Conservation laws Heat fluctuations: theorems and results Bounded perturbations Conclusions

Heat fluctuations Context: quantum statistical mechanics in the two-time measurement framework and Fluctuation relations ultraviolet regularity Annalisa Panati, CPT, Université de Toulon Plan Context: quantum Classical case: [Evans-Cohen-Morris ’93] numerical experiences statistical mechanics [Evans-Searls ’94] [Gallavotti Cohen ’94] theoretical explanation Fluctuation relations Two-time measurment statistics Conservation laws Heat fluctuations: theorems and results Bounded perturbations Conclusions

Heat fluctuations Context: quantum statistical mechanics in the two-time measurement framework and Fluctuation relations ultraviolet regularity Annalisa Panati, CPT, Université de Toulon Plan Context: quantum Classical case: [Evans-Cohen-Morris ’93] numerical experiences statistical mechanics [Evans-Searls ’94] [Gallavotti Cohen ’94] theoretical explanation Fluctuation relations Two-time Statistical refinement of thermodynamics second law measurment statistics Conservation laws Heat fluctuations: theorems and results Bounded perturbations Conclusions

Heat fluctuations Context: quantum statistical mechanics in the two-time measurement framework and Fluctuation relations ultraviolet regularity Annalisa Panati, CPT, Université de Toulon Plan Context: quantum Classical case: [Evans-Cohen-Morris ’93] numerical experiences statistical mechanics [Evans-Searls ’94] [Gallavotti Cohen ’94] theoretical explanation Fluctuation relations Two-time Statistical refinement of thermodynamics second law measurment statistics Conservation laws work in driven system [Bochkov-Kuzovlev ’70s] [Jaryzinski ’97] Heat fluctuations: [Crooks ’99] etc theorems and results Bounded perturbations Conclusions

Heat fluctuations Context: quantum statistical mechanics in the two-time measurement framework and Fluctuation relations ultraviolet regularity Annalisa Panati, CPT, Université de Toulon Plan Context: quantum Classical case: [Evans-Cohen-Morris ’93] numerical experiences statistical mechanics [Evans-Searls ’94] [Gallavotti Cohen ’94] theoretical explanation Fluctuation relations Two-time Statistical refinement of thermodynamics second law measurment statistics Conservation laws work in driven system [Bochkov-Kuzovlev ’70s] [Jaryzinski ’97] Heat fluctuations: [Crooks ’99] etc theorems and results Bounded perturbations Quantum case: ?? Conclusions

Heat fluctuations Quantization of fluctuation relations in the two-time measurement framework and ultraviolet regularity Quantum case: Annalisa Panati, CPT, Université Attempt 1: "Naive quantization" de Toulon Underlying idea : define an observable Σ t = 1 t ( S t − S ) on H and Plan consider the spectral measure µ Σ t Context: quantum statistical mechanics Fluctuation relations Two-time measurment statistics Conservation laws Heat fluctuations: theorems and results Bounded perturbations Conclusions

Heat fluctuations Quantization of fluctuation relations in the two-time measurement framework and ultraviolet regularity Quantum case: Annalisa Panati, CPT, Université Attempt 1: "Naive quantization" de Toulon Underlying idea : define an observable Σ t = 1 t ( S t − S ) on H and Plan consider the spectral measure µ Σ t Context: quantum —attempted in work related litterature [Bochkov-Kuzovlev statistical mechanics ’70s-’80s]) Fluctuation relations —attempted in the ’90, called "naive quantization" Two-time measurment statistics Conservation laws Heat fluctuations: theorems and results Bounded perturbations Conclusions

Heat fluctuations Quantization of fluctuation relations in the two-time measurement framework and ultraviolet regularity Quantum case: Annalisa Panati, CPT, Université Attempt 1: "Naive quantization" de Toulon Underlying idea : define an observable Σ t = 1 t ( S t − S ) on H and Plan consider the spectral measure µ Σ t Context: quantum —attempted in work related litterature [Bochkov-Kuzovlev statistical mechanics ’70s-’80s]) Fluctuation relations —attempted in the ’90, called "naive quantization" Two-time measurment statistics leads to NO-fluctuation relations !!!! Conservation laws Heat fluctuations: theorems and results Bounded perturbations Conclusions

Heat fluctuations Quantization of fluctuation relations in the two-time measurement framework and ultraviolet regularity Quantum case: Annalisa Panati, CPT, Université Attempt 1: "Naive quantization" de Toulon Underlying idea : define an observable Σ t = 1 t ( S t − S ) on H and Plan consider the spectral measure µ Σ t Context: quantum —attempted in work related litterature [Bochkov-Kuzovlev statistical mechanics ’70s-’80s]) Fluctuation relations —attempted in the ’90, called "naive quantization" Two-time measurment statistics leads to NO-fluctuation relations !!!! Conservation laws Heat fluctuations: theorems and Attempt 2: Measurement has ben neglected. Associate to S the results two-time measurment statistics P S t defined as difference between Bounded perturbations Conclusions two measurement

Heat fluctuations Quantization of fluctuation relations in the two-time measurement framework and ultraviolet regularity Quantum case: Annalisa Panati, CPT, Université Attempt 1: "Naive quantization" de Toulon Underlying idea : define an observable Σ t = 1 t ( S t − S ) on H and Plan consider the spectral measure µ Σ t Context: quantum —attempted in work related litterature [Bochkov-Kuzovlev statistical mechanics ’70s-’80s]) Fluctuation relations —attempted in the ’90, called "naive quantization" Two-time measurment statistics leads to NO-fluctuation relations !!!! Conservation laws Heat fluctuations: theorems and Attempt 2: Measurement has ben neglected. Associate to S the results two-time measurment statistics P S t defined as difference between Bounded perturbations Conclusions two measurement

Heat fluctuations Quantization of fluctuation relations in the two-time measurement framework and ultraviolet regularity Quantum case: Annalisa Panati, CPT, Université Attempt 1: "Naive quantization" de Toulon Underlying idea : define an observable Σ t = 1 t ( S t − S ) on H and Plan consider the spectral measure µ Σ t Context: quantum —attempted in work related litterature [Bochkov-Kuzovlev statistical mechanics ’70s-’80s]) Fluctuation relations —attempted in the ’90, called "naive quantization" Two-time measurment statistics leads to NO-fluctuation relations !!!! Conservation laws Heat fluctuations: theorems and Attempt 2: Measurement has ben neglected. Associate to S the results two-time measurment statistics P S t defined as difference between Bounded perturbations Conclusions two measurement

Heat fluctuations Quantization of fluctuation relations in the two-time measurement framework and ultraviolet regularity Quantum case: Annalisa Panati, CPT, Université Attempt 1: "Naive quantization" de Toulon Underlying idea : define an observable Σ t = 1 t ( S t − S ) on H and Plan consider the spectral measure µ Σ t Context: quantum —attempted in work related litterature [Bochkov-Kuzovlev statistical mechanics ’70s-’80s]) Fluctuation relations —attempted in the ’90, called "naive quantization" Two-time measurment statistics leads to NO-fluctuation relations !!!! Conservation laws Heat fluctuations: theorems and Attempt 2: Measurement has ben neglected. Associate to S the results two-time measurment statistics P S t defined as difference between Bounded perturbations Conclusions two measurement —Key result by [Kurchan’00] leads to fluctuation relations