Arcsine Laws in Stochastic Thermodynamics

Arcsine Laws and Interval Partitions Derived from a Stable Subordinator

Le"vy discovered that the fraction of time a standard one-dimensional Brownian motion B spends positive before time t has arcsine distribution, both for / a fixed time when B, # 0 almost surely, and for / an inverse local time, when B, = 0 almost surely. This identity in distribution is extended from the fraction of time spent positive to a large collection of functionals derived from the lengt...

Optimal processes in Stochastic Thermodynamics

B 5 Stochastic thermodynamics

2 Principles 4 2.1 Stochastic dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 First law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Entropy production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Jarzynski relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Optimal finite-t...

Thermodynamics, Statistical Physics and Their Laws

Contents 1. Introduction: On the nature and importance of thermodynamic laws 2. Thermodynamic systems and their description 2.1.

The second laws of quantum thermodynamics

The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the sec...