Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linearresponse variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linearresponse-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently conjectured uncertainty bound on the variance of current fluctuations. DOI: 10.1103/PhysRevLett.116.120601 One of the most useful insights into thermodynamics has been that fluctuations near equilibrium are completely characterized by just one principle: the fluctuationdissipation theorem [1]. Far from equilibrium, however, fluctuations exhibit less universal structure. As such, characterizing the rich anatomy of nonequilibrium fluctuations has been handled on a case by case basis, with few universal nonequilibrium principles. Notable exceptions are the fluctuation theorems [2][3][4][5][6][7], as well as fluctuationdissipation theorems for nonequilibrium steady states [8][9][10][11][12]. Recently, Barato and Seifert have proposed a new kind of nonequilibrium principle, a thermodynamic uncertainty relation that expresses a trade-off between the variance of current fluctuations and the rate of entropy production [13]. It reveals that away from equilibrium, dissipation continues to regulate small fluctuations. While the thermodynamic uncertainty relation was not proven in general, analytical calculations and numerical evidence support its validity [13]. Applications appear myriad, and already include insights into chemical kinetics as well as biochemical sensing [14,15].In this Letter, we demonstrate that dissipation in fact constrains all current fluctuations. In particular, we prove a pair of general thermodynamic inequalities for the large deviation function of the steady-state empirical currents in Markov jump processes. Such processes model a variety of scenarios, including molecular motors [16], chemical reaction networks [17,18], and mesoscopic quantum devices [19]. Our analysis reveals that far from equilibrium, current fluctuations are always more probable than would be predicted by linear response [20,21]. Remarkably, our relationship bounds even rare fluctuations (large deviations), and by specializing to small deviations we obtain the thermodynamic uncertainty relation.We have in mind a system with N mesoscopic states (or configurations), x ¼ 1; …; N. Transitions between pairs of states, say from y to z, are modeled as a continuous-time Markov jump process with rates rðy; zÞ [22]. It is convenient to picture these dynamics occurring on a graph (as in Fig. 1), with vertices denoting states and edges (or links) symbolizing possible transitions. We assume the dynamics to be ergodic and that rðz; yÞ > 0 whenever rðy; zÞ > 0, so ...

Whether by virtue of being prepared in a slowly relaxing, high-free energy initial condition, or because they are constantly dissipating energy absorbed from a strong external drive, many systems subject to thermal fluctuations are not expected to behave in the way they would at thermal equilibrium. Rather, the probability of finding such a system in a given microscopic arrangement may deviate strongly from the Boltzmann distribution, raising the question of whether thermodynamics still has anything to tell us about which arrangements are the most likely to be observed. In this work, we build on past results governing nonequilibrium thermodynamics and define a generalized Helmholtz free energy that exactly delineates the various factors that quantitatively contribute to the relative probabilities of different outcomes in far-fromequilibrium stochastic dynamics. By applying this expression to the analysis of two examples-namely, a particle hopping in an oscillating energy landscape and a population composed of two types of exponentially growing self-replicators-we illustrate a simple relationship between outcome-likelihood and dissipative history. In closing, we discuss the possible relevance of such a thermodynamic principle for our understanding of self-organization in complex systems, paying particular attention to a possible analogy to the way evolutionary adaptations emerge in living things.

Various studies suggest that the hydrophobic effect plays a major role in driving the folding of proteins. In the past, however, it has been challenging to translate this understanding into a predictive, quantitative theory of how the full pattern of sequence hydrophobicity in a protein shapes functionally important features of its tertiary structure. Here, we extend and apply such a phenomenological theory of the sequence-structure relationship in globular protein domains, which had previously been applied to the study of allosteric motion. In an effort to optimize parameters for the model, we first analyze the patterns of backbone burial found in singledomain crystal structures, and discover that classic hydrophobicity scales derived from bulk physicochemical properties of amino acids are already nearly optimal for prediction of burial using the model. Subsequently, we apply the model to studying structural fluctuations in proteins and establish a means of identifying ligand-binding and protein-protein interaction sites using this approach.