Reference : Stochastic Thermodynamics for Underdamped Brownian Particles: Equivalent Measures, Re...
Dissertations and theses : Doctoral thesis
Physical, chemical, mathematical & earth Sciences : Physics
Physics and Materials Science
Stochastic Thermodynamics for Underdamped Brownian Particles: Equivalent Measures, Reversed Stochastic Processes and Feynman-Kac Techniques
Shayanfard, Kamran mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit >]
University of Luxembourg, ​​Luxembourg
Docteur en Physique
Esposito, Massimiliano mailto
[en] Underdamped Stochastic Thermodynamics ; Equivalent Measures ; Feynman-Kac ; Fluctuation Theorem ; Generating Function
[en] Underdamped stochastic thermodynamics provides a handy tool to study a large
class of stochastic processes operating out of equilibrium. Colloidal particles in
a laser trap, molecular motors and feedback processes are some of the prominent
examples. In the present work we give a mathematical framework for the study
of the thermodynamic properties of these phenomena. We focus on Markovian
stochastic processes in continuous time and space, and show how the techniques
of equivalent measures combined with stochastic solutions of partial differential
equations, obtained through Feynman-Kac formula, can be used to derive exact
relations between forward and backward diffusion processes. We prove a theorem
which allows us to derive the time evolution of an arbitrary path quantity in a
simple and systematic way. We further consider a fairly general underdamped
stochastic model, and study its nonequilibrium thermodynamic properties at both
single trajectory and average levels. For this model, we establish several integral
and detailed fluctuation theorems for thermodynamic quantities such as work and
entropy production, amongst others. Some of these theorems directly parallel
those already obtained in the context of overdamped and master equations, while
others are novel. We also discuss some special cases of our model which are directly
related to physical systems such as active Brownian particles, feedback processes
and isoenergetic stochastic processes. The formalism we develop, and the general
model considered here constitute a unified and extended framework for the study
of the thermodynamics of underdamped processes, encompassing several physical
systems and applications.

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