Longest Relaxation Time of Relaxation Processes for Classical and Quantum Brownian Motion in a Potential: Escape Rate Theory Approach

2013 ◽  
pp. 111-309 ◽  
Author(s):  
William T. Coffey ◽  
Yuri P. Kalmykov ◽  
Serguey V. Titov ◽  
William J. Dowling
Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1602
Author(s):  
Jin-Fu Chen ◽  
Tian Qiu ◽  
Hai-Tao Quan

Quantum Brownian motion, described by the Caldeira–Leggett model, brings insights to the understanding of phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum–classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat and its long-time limit reflects the complete thermalization of the system. Our research study justifies the definition of the quantum fluctuating heat via two-point measurements.


1954 ◽  
Vol 27 (1) ◽  
pp. 36-54 ◽  
Author(s):  
W. Kuhn ◽  
O. Künzle ◽  
A. Preissmann

Abstract By rapid deformation of a medium in which linear molecules are present, various changes are produced simultaneously in the latter. These changes are more or less independent of one another, and can release independently and totally or partially by rearrangement of valence distances and valence angles in the chain molecules. By virtue of such relaxation processes, a portion of the stress originating in the rapid deformation disappears, with a changing time requirement for the various portions. A relaxation time spectrum is thus formed. The relaxation time spectrum consists of a finite number of restoring force mechanisms with proper relaxation times or of a continuous spectrum. Both the creep curves (the dependence of the length of a body on time at constant load), and stress relaxation (decay of the stress observed in test sample kept at constant length after rapid deformation), as well as the total visco-elastic behavior, especially the behavior at constant periodic deformation of the test sample, are determined by the relaxation time spectrum. The appropriate Quantitative relationships were derived.


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