3 research outputs found
Effective thermodynamics of two interacting underdamped Brownian particles
Starting from the stochastic thermodynamics description of two coupled
underdamped Brownian particles, we showcase and compare three different
coarse-graining schemes leading to an effective thermodynamic description for
the first of the two particles: marginalization over one particle, bipartite
structure with information flows and the Hamiltonian of mean force formalism.
In the limit of time-scale separation where the second particle with a fast
relaxation time scale locally equilibrates with respect to the coordinates of
the first slowly relaxing particle, the effective thermodynamics resulting from
the first and third approach are shown to capture the full thermodynamics and
to coincide with each other. In the bipartite approach, the slow part does not,
in general, allow for an exact thermodynamic description as the entropic
exchange between the particles is ignored. Physically, the second particle
effectively becomes part of the heat reservoir. In the limit where the second
particle becomes heavy and thus deterministic, the effective thermodynamics of
the first two coarse-graining methods coincides with the full one. The
Hamiltonian of mean force formalism however is shown to be incompatible with
that limit. Physically, the second particle becomes a work source. These
theoretical results are illustrated using an exactly solvable harmonic model.Comment: 18 pages, 4 figure
Stochastic Thermodynamics for Underdamped Brownian Particles: Equivalent Measures, Reversed Stochastic Processes and Feynman-Kac Techniques
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