arXiv subjects

Supriya Krishnamurthy

Publications and source records attributed to Supriya Krishnamurthy.

At least 19 recordsLinked to original sources

arXiv2026

Signatures of coherent initial ensembles on all work moments

Standard treatments of quantum work using projective energy measurements erase initial coherence and alter the dynamics, thereby failing to capture the thermodynamic effects of coherent superpositions of energy eigenstates in an ensemble of initial states. In this article, we use an operational work definition that is non-intrusive, applying it to the case of a driven dissipative qubit, where the qubit's initial preparation comprises coherent superposition states, while the driving is coherence-less. We derive an evolution equation for the moment generating function for this work, faithfully capturing the thermodynamic signature of coherent superpositions in the initial ensemble. We demonstrate that different initial ensembles that correspond to the same density matrix upon ensemble average, while having the same average work, display different work fluctuations. For monotonic driving, we show that fluctuations are maximum for coherence-less initial ensembles. As an application, we consider quantum bit-erasure in finite time and demonstrate significantly different work statistics for erasing a classical bit of information versus a Haar random initial ensemble. Our results indicate that coherence in the initial ensemble can be utilized as a resource for thermodynamic precision without incurring additional dissipative work costs. We also obtain a generalized fluctuation theorem that establishes a new quantum lower bound on the mean dissipated work. This bound, counterintuitively, is also applicable to a "classical" initial ensemble with the same initial density matrix and is connected to quantum absolute irreversibility.

quant-ph↗

arXiv2025

Thermodynamic Cost of Recurrent Erasure

Recent experiments have implemented resetting by means of a time-varying external harmonic trap whereby the trap stiffness is changed from an initial to a final value in finite-time and then the system is reset when it relaxes to an equilibrium distribution in the final trap. Such setups are very similar to those studied in the context of the finite-time Landauer erasure principle. We analyze the thermodynamic costs of such a setup by deriving a moment generating function for the work cost of recurrently changing the trap stiffness in finite-time, thereby maintaining a non-equilibrium steady state. We analyze the mean and variance of the work required for a specific experimentally viable protocol and also obtain an optimal protocol which minimizes the mean cost. For both these procedures, our analysis captures both the large-time and short-time corrections. For the optimal protocol, we obtain a closed form expression for the mean cost for all protocol durations, thereby making contact with earlier work on geometric measures of dissipation-minimizing optimal protocols that implement information erasure.

cond-mat.stat-mech↗

arXiv2024

Irreversibility of mesoscopic processes with hydrodynamic interactions

Optically confined colloidal particles, when placed in close proximity, form a dissipatively coupled system through hydrodynamic interactions. The role of such interactions influencing irreversibility and energy dissipation in out-of-equilibrium systems is often not well deciphered. Here, we demonstrate - through the estimation of the entropy production rate - that the nonequilibrium features of the system with such interactions vary depending on the nature of external driving, and importantly, on the level of coarse-graining. Crucially, we show that coarse-graining reverses the dependence of the measured entropy production rate on the strength of the hydrodynamic interactions. Furthermore, we clarify that such interactions do not violate energy balance at the level of individual trajectories, as was believed earlier. Our results highlight a previously unnoticed effect of coarse-graining in nonequilibrium systems, and have implications for the inference of entropy production in experimental contexts.

cond-mat.stat-mech↗

arXiv2023

Thermodynamic cost of finite-time stochastic resetting

Recent experiments have implemented resetting by means of an external trap, whereby a system relaxes to the minimum of the trap and is reset in a finite time. In this work, we set up and analyse the thermodynamics of such a protocol. We present a general framework, even valid for non-Poissonian resetting, that captures the thermodynamic work required to maintain a resetting process up to a given observation time, and exactly calculate the moment generating function of this work. Our framework is valid for a wide range of systems, the only assumption being relaxation to equilibrium in the resetting trap. Examples and extensions are considered. In the case of Brownian motion, we investigate optimal resetting schemes that minimise work and its fluctuations, the mean work for arbitrary switching protocols and comparisons to previously studied resetting schemes. Numerical simulations are performed to validate our findings.

cond-mat.stat-mech↗

arXiv2022

Entropy production of resetting processes

Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and in experiments. Oftentimes, however, resetting to a fixed state is impossible due to thermal noise or other limitations. As a result, the system configuration after a resetting event is random. Here, we consider such a resetting protocol for an overdamped Brownian particle in a confining potential $V(x)$. We assume that the position of the particle is reset at a constant rate to a random location $x$, drawn from a distribution $p_R(x)$. To investigate the thermodynamic cost of resetting, we study the stochastic entropy production $S_{\rm Total}$. We derive a general expression for the average entropy production for any $V(x)$, and the full distribution $P(S_{\rm Total}|t)$ of the entropy production for $V(x)=0$. At late times, we show that this distribution assumes the large-deviation form $P(S_{\rm Total}|t)\sim \exp\left[-t^{2\alpha-1}\phi\left(\left(S_{\rm Total}-\langle S_{\rm Total}\rangle\right)/t^{\alpha}\right)\right]$, with $1/2<\alpha\leq 1$. We compute the rate function $\phi(z)$ and the exponent $\alpha$ for exponential and Gaussian resetting distributions. In the latter case, we find the anomalous exponent $\alpha=2/3$ and show that $\phi(z)$ has a first-order singularity at a critical value of $z$, corresponding to a real-space condensation transition.

cond-mat.stat-mech↗

arXiv2022

Non-monotonic skewness of currents in non-equilibrium steady states

Measurements of any property of a microscopic system are bound to show significant deviations from the average, due to thermal fluctuations. For time-integrated currents such as heat, work or entropy production in a steady state, it is in fact known that there will be long stretches of fluctuations both above as well as below the average, occurring equally likely at large times. In this paper we show that for any finite-time measurement in a non-equilibrium steady state - rather counter-intuitively - fluctuations below the average are more probable. This discrepancy is higher when the system is further away from equilibrium. For overdamped diffusive processes, there is even an optimal time when time-integrated current fluctuations mostly lie below the average. We demonstrate that these effects result from the non-monotonic skewness of current fluctuations and provide evidence that they are easily observable in experiments. We also discuss their extensions to discrete space Markov jump processes and implications to biological and synthetic microscopic engines.

cond-mat.stat-mech↗

arXiv2021

Quantitative analysis of non-equilibrium systems from short-time experimental data

We provide a minimal strategy for the quantitative analysis of a large class of non-equilibrium systems in a {statistically} steady state using the short-time Thermodynamic Uncertainty Relation (TUR). From short-time trajectory data obtained from experiments, we demonstrate how we can simultaneously infer quantitatively, both the thermodynamic force field acting on the system, as well as the (potentially exact) rate of entropy production. We benchmark this scheme first for an experimental study of a colloidal particle system where exact analytical results are known, before applying it to the case of a colloidal particle in a hydrodynamical flow field, where neither analytical nor numerical results are available. In this latter case, we build an effective model of the system based on our results. In both cases, we also demonstrate that our results match with those obtained from another recently introduced scheme [Phys. Rev. X 10, 021009].

cond-mat.soft↗

arXiv2021

Estimating time-dependent entropy production from non-equilibrium trajectories

The rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary dynamics, some of which are based on a variational characterization of the entropy production rate. However, the issue of obtaining it in the case of non-stationary dynamics remains largely unexplored. Here, we solve this open problem by demonstrating that the variational approaches can be generalized to give the exact value of the entropy production rate even for non-stationary dynamics. On the basis of this result, we develop an efficient algorithm that estimates the entropy production rate continuously in time by using machine learning techniques, and validate our numerical estimates using analytically tractable Langevin models in experimentally relevant parameter regimes. Our method is of great practical significance since all it requires is time-series data for the system of interest without requiring prior knowledge of the system parameters.

cond-mat.stat-mech↗

arXiv2020

Eikonal solutions for moment hierarchies of Chemical Reaction Networks in the limits of large particle number

Trajectory-based methods are well-developed to approximate steady-state probability distributions for stochastic processes in large-system limits. The trajectories are solutions to equations of motion of Hamiltonian dynamical systems, and are known as eikonals. They also express the leading flow lines along which probability currents balance. The existing eikonal methods for discrete-state processes including chemical reaction networks are based on the Liouville operator that evolves generating functions of the underlying probability distribution. We have previously derived a representation for the generators of such processes that acts directly in the hierarchy of moments of the distribution, rather than on the distribution itself or on its generating function. We show here how in the large-system limit the steady-state condition for that generator reduces to a mapping from eikonals to the ratios of neighboring factorial moments, as a function of the order $k$ of these moments. The construction shows that the boundary values for the moment hierarchy, and thus its whole solution, are anchored in the interior fixed points of the Hamiltonian system, a result familiar from Freidlin-Wenztell theory. The direct derivation of eikonals from the moment representation further illustrates the relation between coherent-state and number fields in Doi-Peliti theory, clarifying the role of canonical transformations in that theory.

cond-mat.stat-mech↗

arXiv2020

Inferring entropy production from short experiments

We provide a strategy for an exact inference of the average as well as the fluctuations of the entropy production in non-equilibrium systems in the steady state, from the measurements of arbitrary current fluctuations. Our results are built upon the finite time generalization of the thermodynamic uncertainty relation, and require only very short time series data from experiments. We illustrate our results with exact and numerical solutions for two colloidal heat engines.

cond-mat.stat-mech↗

arXiv2019

Efficiency fluctuations in microscopic machines

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a `universal theory of efficiency fluctuations' at long times, for machines with a finite state space, was developed in [Verley \textit{et al.}, Nat.~Commun.~\textbf{5}, 4721 (2014); Phys.~Rev.~E~\textbf{90}, 052145 (2014)]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the `universal features' and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two non-trivial models of colloidal engines.

cond-mat.stat-mech↗

arXiv2018

Path-reversal, Doi-Peliti generating functionals, and dualities between dynamics and inference for stochastic processes

Fluctuation theorems may be partitioned into those that apply the probability measure under the original stochastic process to reversed paths, and those that construct a new, adjoint measure by similarity transform, which locally reverses probability currents. Results that use the original measure have a natural interpretation in terms of time-reversal of the dynamics. Here we develop a general interpretation of fluctuation theorems based on the adjoint process by considering the duality of the Kolmogorov-forward and backward equations, acting on distributions versus observables. The backward propagation of the dependency of observables is related to problems of statistical inference, so we characterize the adjoint construction as a duality between dynamics and inference. The adjoint process corresponds to the Kolmogorov backward equation in a generating functional that erases memory from the dynamics of its underlying distribution. We show how erasure affects general correlation functions by showing that duality under the adjoint fluctuation theorems exchanges the roles of advanced and retarded Green's functions. We derive results for the class of discrete-state stochastic processes corresponding to Chemical Reaction Networks (CRNs), and show that dualization acts on the \emph{finite} representation of the generating event-set, in a manner similar to the usual similarity transform acting on the (potentially infinite) set of state transitions. We construct generating functionals within the Doi-Peliti (DP) functional integral framework, within which duality transformation takes a remarkably simple form as a change of integration variable. Our Green's function analysis recovers the Extended Fluctuation-Dissipation Theorem of Seifert and Speck for non-equilibrium steady states, shows that the causal structure responsible for it applies also to dualization about non-steady states.

cond-mat.stat-mech↗

arXiv2018

Exact results for the finite time thermodynamic uncertainty relation

We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of the dissipated work at arbitrary times. The uncertainty function (the Fano factor of the dissipated work) is bounded from below by $2k_BT$ as expected, for all times $τ$, in both steady state and transient regimes. The lower bound is reached at $τ=0$ as well as when certain system parameters vanish (corresponding to an equilibrium state). Surprisingly, we find that the uncertainty function also reaches a constant value at large $τ$ for all the cases we have looked at. For a system starting and remaining in steady state, the uncertainty function increases monotonically, as a function of $τ$ as well as other system parameters, implying that the large $τ$ value is also an upper bound. For the same system in the transient regime, however, we find that the uncertainty function can have a local minimum at an accessible time $τ_m$, for a range of parameter values. The non-monotonicity suggests, rather counter-intuitively, that there might be an optimal time for the working of microscopic machines, as well as an optimal configuration in the phase space of parameter values. Our solutions show that the ratios of higher moments of the dissipated work are also bounded from below by $2k_BT$. For another model, also solvable by our methods, which never reaches a steady state, the uncertainty function, is in some cases, bounded from below by a value less than $2k_BT$.

cond-mat.stat-mech↗

arXiv2017

Asymptotics of work distributions in a stochastically driven system

We determine the asymptotic forms of work distributions at arbitrary times $T$, in a class of driven stochastic systems using a theory developed by Engel and Nickelsen (EN theory) (arXiv:1102.4505v1 [cond-mat.stat-mech]), which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in the path integral form, are characterised by having quadratic actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks flucutation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial function. We then extend our analysis to a stochastically driven system, studied in ( arXiv:1212.0704v2 [cond-mat.stat-mech], arXiv:1402.5777v1 [cond-mat.stat-mech]) using a moment-generating-function method, for both equilibrium and non - equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary $T$. For dissipated work in the steady state, we compare the large $T$ asymptotic behaviour of our solution to that already obtained in ( arXiv:1402.5777v1 [cond-mat.stat-mech]). In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with the numerical simulations. Our solutions are exact in the low noise limit.

cond-mat.stat-mech↗

arXiv2017

Solving Moment Hierarchies for Chemical Reaction Networks

The study of Chemical Reaction Networks (CRN's) is a very active field. Earlier well-known results \cite{Feinberg:def_01:87, Anderson:product_dist:10} identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. In this paper, we show how to write the full moment-hierarchy for any non-zero-deficiency CRN obeying mass-action kinetics, in terms of equations for the factorial moments (FM). Using these, we can recursively predict values for lower moments from higher moments, reversing the procedure usually used to solve moment hierarchies. We show, for non-trivial examples, that in this manner we can predict to high accuracy, any moment of interest, for CRN's with non-zero deficiency and non-factorizable steady states.

cond-mat.stat-mech↗

arXiv2017

Flows, scaling, and the control of moment hierarchies for stochastic chemical reaction networks

Stochastic chemical reaction networks (CRNs) are complex systems which combine the features of concurrent transformation of multiple variables in each elementary reaction event, and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes value 0 or 1. Here we derive equations of motion for fluctuation moments at all orders for stochastic CRNs at general deficiency. We show, for the case of the mass-action rate law, that the generator of the stochastic process acts on the hierarchy of factorial moments with a finite representation. Whereas simulation of high-order moments for many-particle systems is costly, this representation reduces solution of moment hierarchies to a complexity comparable to solving a heat equation. At steady states, moment hierarchies for finite CRNs interpolate between low-order and high-order scaling regimes, which may be approximated separately by distributions similar to those for deficiency-0 networks, and connected through matched asymptotic expansions. In CRNs with multiple stable or metastable steady states, boundedness of high-order moments provides the starting condition for recursive solution downward to low-order moments, reversing the order usually used to solve moment hierarchies. A basis for a subset of network flows defined by having the same mean-regressing property as the flows in deficiency-0 networks gives the leading contribution to low-order moments in CRNs at general deficiency, in a $1/n$-expansion in large particle numbers. Our results give a physical picture of the different informational roles of mean-regressing and non-mean-regressing flows, and clarify the dynamical meaning of deficiency not only for first-moment conditions but for all orders in fluctuations.

physics.chem-ph↗

arXiv2014

An alternate view of complexity in k-SAT problems

The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large system limit. Two different approaches to obtaining this threshold have been discussed in the literature - using first or second-moment methods which give rigorous bounds or using the non-rigorous but powerful replica-symmetry breaking (RSB) approach, which gives very accurate predictions on random graphs. In this paper, we lay out a different route to obtaining this threshold on a Bethe lattice. We need make no assumptions about the solution-space structure, a key assumption in the RSB approach. Despite this, our expressions and threshold values exactly match the best predictions of the cavity method under the 1-RSB assumption. Our method hence provides alternate interpretations as well as motivations for the key equations in the RSB approach.

cond-mat.stat-mech↗

arXiv2012

Balanced K-SAT and Biased random K-SAT on trees

We study and solve some variations of the random K-satisfiability problem - balanced K-SAT and biased random K-SAT - on a regular tree, using techniques we have developed earlier(arXiv:1110.2065). In both these problems, as well as variations of these that we have looked at, we find that the SAT-UNSAT transition obtained on the Bethe lattice matches the exact threshold for the same model on a random graph for K=2 and is very close to the numerical value obtained for K=3. For higher K it deviates from the numerical estimates of the solvability threshold on random graphs, but is very close to the dynamical 1-RSB threshold as obtained from the first non-trivial fixed point of the survey propagation algorithm.

cond-mat.stat-mech↗