Excerpt

Introduction

The discovery of different fluctuation theorems (FTs) over the last two decades constitutes major progress in nonequilibrium physics (Harris and Schütz 2007; Esposito, Harbola, and Mukamel 2009; Jarzynski 2011; Campisi, Hänggi, and Talkner 2011; Seifert 2012; Van den Broeck and Esposito 2015). These relations are exact constraints that some fluctuating quantities satisfy arbitrarily far from equilibrium. They have been verified experimentally in many different contexts, ranging from biophysics to electronic circuits (Ciliberto 2017). However, they come in different forms—detailed fluctuation theorems (DFTs) or integral fluctuation theorems (IFTs)—and concern various types of quantities. Understanding how they are related and to what extent they involve mathematical quantities or interesting physical observables can be challenging.

The plan of the chapter is as follows. Time-inhomogeneous Markov jump processes are introduced in the following section. Our main results are presented in the third section: we first introduce the EP as a quantifier of detailed balance breaking, and we then show that, by choosing a reference PMF, EP splitting ensues. This enables us to identify the fluctuating quantities satisfying a DFT and an IFT when the system is initially prepared in the reference PMF. Whereas IFTs hold for arbitrary reference PMFs, DFTs require reference PMFs to be determined solely by the driving protocol encoding the time dependence of the rates. The EP decomposition is also shown to lead to a generalized Landauer principle. The remaining sections are devoted to specific reference PMFs and show that they give rise to interesting mathematics or physics: first, the steady-state PMF of the Markov jump process is chosen, giving rise to the adiabatic–nonadiabatic split of the EP (Esposito, Harbola, and Mukamel 2007); then, the equilibrium PMF of a spanning tree of the graph defined by the Markov jump process is chosen and gives rise to a cycle–cocycle decomposition of the EP (Polettini 2014). Physics is introduced next, and the properties that the Markov jump process must satisfy to describe the thermodynamics of an open system are described. In the next section, the microcanonical distribution is chosen as the reference PMF leading to the splitting of the EP into system and reservoir entropy change. Finally, the generalized Gibbs equilibrium PMF is chosen as a reference and leads to a conservative–nonconservative splitting of the EP (Rao and Esposito 2018b). Conclusions are drawn in the final section, and some technical proofs are discussed in appendices.

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