Three detailed fluctuation theorems

The total entropy production of a trajectory can be split into an adiabatic and a non-adiabatic contribution, deriving respectively from the breaking of detailed balance via nonequilibrium boundary conditions or by external driving. We show that each of them, the total, the adiabatic and the non-adiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.Comment: 4 pages, V2: accepted in Phys. Rev. Lett. 104, 090601 (2010

Discrete-time thermodynamic uncertainty relation

We generalize the thermodynamic uncertainty relation, providing an entropic upper bound for average fluxes in time-continuous steady-state systems (Gingrich et al., Phys. Rev. Lett. 116, 120601 (2016)), to time-discrete Markov chains and to systems under time-symmetric, periodic driving

Ensemble and Trajectory Thermodynamics: A Brief Introduction

We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.Comment: Course given by C. Van den Broeck at the Summer School "Fundamental Problems in Statistical Physics XIII", June 16-29, 2013 Leuven, Belgium; V2: version accepted in Physica A (references improved + other minor changes

Phase transitions in persistent and run-and-tumble walks

We calculate the large deviation function of the end-to-end distance and the corresponding extension-versus-force relation for (isotropic) random walks, on and off-lattice, with and without persistence, and in any spatial dimension. For off-lattice random walks with persistence, the large deviation function undergoes a first order phase transition in dimension $d> 5$. In the corresponding force-versus-extension relation, the extension becomes independent of the force beyond a critical value. The transition is anticipated in dimensions $d=4$ and $d=5$, where full extension is reached at a finite value of the applied stretching force. Full analytic details are revealed in the run-and-tumble limit. Finally, on-lattice random walks with persistence display a softening phase in dimension $d=3$ and above, preceding the usual stiffening appearing beyond a critical value of the force