Stochastic functionals and fluctuation theorem for multikangaroo processes

Abstract

We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.

Stochastic thermodynamics for linear kinetic equations

“…We derive the fluctuation theorem, including a new version expressed only in terms of probabilities computed from the forward process. As an application, we provide explicit illustrations for the special case of kinetic "kangaroo" equations [14,15]. The role of a general parity symmetry condition similar to the one used here has also recently been pointed out in the context of the quantum Jarzynski equality [16], in the sense that the equality does not hold if parity is violated.…”

“…To illustrate the above formalism, we focus on the simple case of a "kangaroo" kinetic equation with a rate k(v → v) [15]:…”

“…We derive the fluctuation theorem, including a new version expressed only in terms of probabilities computed from the forward process. As a application, we provide explicit illustrations for the special case of kinetic "kangaroo" equations [14].…”

“…which can conveniently be verified by considering statistics of the forward experiment alone. To illustrate the above formalism, we focus on the simple case of a "kangaroo" kinetic equation with a rate k(v → v) [14]:…”