Todd R. Gingrich

Dissipation bounds all steady-state current fluctuations

Near equilibrium, small current fluctuations are described by a Gaussian distribution with a linear-response 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 linear-response-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.

Combinatorial synthesis and high-throughput photopotential and photocurrent screening of mixed-metal oxides for photoelectrochemical water splitting

A high-throughput method has been developed using a commercial piezoelectric inkjet printer for synthesis and characterization of mixed-metal oxide photoelectrode materials for water splitting. The printer was used to deposit metal nitrate solutions onto a conductive glass substrate. The deposited metal nitrate solutions were then pyrolyzed to yield mixed-metal oxides that contained up to eight distinct metals. The stoichiometry of the metal oxides was controlled quantitatively, allowing for the creation of vast libraries of novel materials. Automated methods were developed to measure the open-circuit potentials (Eoc), short-circuit photocurrent densities (Jsc), and current density vs. applied potential (J–E) behavior under visible light irradiation. The high-throughput measurement of Eoc is particularly significant because open-circuit potential measurements allow the interfacial energetics to be probed regardless of whether the band edges of the materials of concern are above, close to, or below the values needed to sustain water electrolysis under standard conditions. The Eoc measurements allow high-throughput compilation of a suite of data that can be associated with the composition of the various materials in the library, to thereby aid in the development of additional screens and to form a basis for development of theoretical guidance in the prediction of additional potentially promising photoelectrode compositions.

Hydroxyapatite chromatography of phage-display virions

Hydroxyapatite column chromatography can be used to purify filamentous bacteriophage--the phage most commonly used for phage display. Virions that have been partially purified from culture supernatant by two cycles of precipitation in 2% polyethylene glycol are adsorbed onto the matrix at a density of at least 7.6 x 10(13) virions (about 3 mg) per milliliter of packed bed volume in phosphate-buffered saline (PBS; 0.15 M NaCl, 5 mM NaH2PO4, pH-adjusted to 7.0 with NaOH). The matrix is washed successively with wash buffer I(150 mM NaCl, 125 mM phosphate, pH 7.0), wash buffer II (2.55 M NaCl, 125 mM phosphate, pH 7.0), and wash buffer I; after which virions are desorbed in desorption buffer (150 mM NaCl, 200 mM phosphate, pH 7.0), and the matrix is stripped with stripping buffer (150 mM NaCl, 1 Mphosphate, pH 7.0). About half of the applied virions are recovered in desorption buffer. Western blot analysis shows that they have undetectable levels of host-derived protein contaminants that are present in the input virions and in virions purified by CsCl equilibrium density gradient centrifugation--the method most commonly used to prepare virions in high purity. Hydroxyapatite chromatography is thus an attractive alternative method for purifying filamentous virions, particularly when the scale is too large for ultracentrifugation to be practical.

Proof of the finite-time thermodynamic uncertainty relation for steady-state currents

The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a recently conjectured finite-time thermodynamic uncertainty relation for steady-state current fluctuations. Our proof is based on a quadratic bound to the large deviation rate function for currents in the limit of a large ensemble of many copies.

Inferring dissipation from current fluctuations

Complex physical dynamics can often be modeled as a Markov jump process between mesoscopic configurations. When jumps between mesoscopic states are mediated by thermodynamic reservoirs, the time-irreversibility of the jump process is a measure of the physical dissipation. We rederive a recently introduced inequality relating the dissipation rate to current fluctuations in jump processes. We then adapt these results to diffusion processes via a limiting procedure, reaffirming that diffusions saturate the inequality. Finally, we study the impact of spatial coarse-graining in a two-dimensional model with driven diffusion. By observing fluctuations in coarse-grained currents, it is possible to infer a lower bound on the total dissipation rate, including the dissipation associated with hidden dynamics. The tightness of this bound depends on how well the spatial coarse-graining detects dynamical events that are driven by large thermodynamic forces.

Efficiency and large deviations in time-asymmetric stochastic heat engines

In a stochastic heat engine driven by a cyclic non-equilibrium protocol, fluctuations in work and heat give rise to a fluctuating efficiency. Using computer simulations and tools from large deviation theory, we have examined these fluctuations in detail for a model two-state engine. We find in general that the form of efficiency probability distributions is similar to those described by Verley et al (2014 Nat. Commun. 5 4721), in particular featuring a local minimum in the long-time limit. In contrast to the time-symmetric engine protocols studied previously, however, this minimum need not occur at the value characteristic of a reversible Carnot engine. Furthermore, while the local minimum may reside at the global minimum of a large deviation rate function, it does not generally correspond to the least likely efficiency measured over finite time. We introduce a general approximation for the finite-time efficiency distribution, , based on large deviation statistics of work and heat, that remains very accurate even when deviates significantly from its large deviation form.

Dynamic phase transitions in simple driven kinetic networks.

We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, where energy fluxes typically result in nonequilibrium dynamics. By analyzing the fluctuations in the entropy production, we demonstrate the emergence, in a large system size limit, of a dynamic phase transition between two distinct dynamical regimes.

Near-optimal protocols in complex nonequilibrium transformations

Significance Classical thermodynamics was developed to help design the best protocols for operating heat engines that remain close to equilibrium at all times. Modern experimental techniques for manipulating microscopic and mesoscopic systems routinely access far-from-equilibrium states, demanding new theoretical tools to describe the optimal protocols in this more complicated regime. Prior studies have sought, in simple models, the protocol that minimizes dissipation. We use computational tools to investigate the diversity of low-dissipation protocols. We show that optimal protocols can be accompanied by a vast set of near-optimal protocols, which still offer the substantive benefits of the optimal protocol. Although solving for the optimal protocol is typically difficult, computationally identifying a near-optimal protocol can be comparatively easy. The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased toward a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.

Fundamental Bounds on First Passage Time Fluctuations for Currents

Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation. Here, we derive a conjugate uncertainty relationship for the first passage time to accumulate a fixed net current. More generally, we use the tools of large-deviation theory to simply connect current fluctuations and first passage time fluctuations in the limit of long times and large currents. With this connection, previously discovered symmetries and bounds on the large-deviation function for currents are readily transferred to first passage times.

Hierarchical bounds on entropy production inferred from partial information

Systems driven away from thermal equilibrium constantly deliver entropy to their environment. Determining this entropy production requires detailed information about the systems internal states and dynamics. However, in most practical scenarios, only a part of a complex experimental system is accessible to an external observer. In order to address this challenge, two notions of partial entropy production have been introduced in the literature as a way to assign an entropy production to an observed subsystem: one due to Shiraishi and Sagawa [Phys. Rev. E 91, 012130 (2015)] and another due to Polettini and Esposito [arXiv:1703.05715 (2017)]. We show that although both of these schemes provide a lower bound on the total entropy production, the latter -- which utilizes an effective thermodynamics description-- gives a better estimate of the total dissipation. Using this effective thermodynamic framework, we establish a partitioning of the total entropy production into two contributions that individually verify integral fluctuation theorems: an observable partial entropy production and a hidden entropy production assigned to the unobserved subsystem. Our results offer broad implications for both theoretical and empirical systems when only partial information is available.