arXiv subjects

Alexander M. Maier

Publications and source records attributed to Alexander M. Maier.

6 recordsLinked to original sources

arXiv2026

Generalizing the multidimensional thermodynamic uncertainty relation to combinations of arbitrary counting variables

Uncertainty relations provide lower bounds for otherwise hidden quantities of a partially accessible Markov network like the mean entropy production rate and the total dynamical activity. The thermodynamic uncertainty relation (TUR) is arguably the most prominent one and involves the precision of a fluctuating net current. One of its major generalizations is the multidimensional TUR (MTUR), which yields a tighter bound by using covariances of a set of observed net currents. We generalize this latter bound to time-dependently driven processes with arbitrary initial state and arbitrary measurement duration. Furthermore, this bound can be used with a set of fluctuating counting observables each of which can be time-antisymmetric, time-symmetric or time-asymmetric, i.e., a net current, a traffic or a flow. We can even allow for coarse-grained observations in which each counting observable could consist of multiple indiscernable observed transitions of the underlying system. Thus, we generalize the MTUR, extensions of the TUR for time-dependent processes based on one current, and an estimator based on one flux or on one traffic in a unifying way. We illustrate this general uncertainty relation with simple examples.

cond-mat.stat-mech↗

arXiv2026

Lower bounds on entropy production from dynamical correlation functions

Entropy production is a key property in stochastic thermodynamics. For partially observed and coarse-grained systems, its inference is challenging and typically rests on proven lower bounds. We derive two versions of such bounds based on the asymmetry of experimentally accessible two-time correlation functions of coarse-grained state observables. For non-equilibrium steady states, the bound is valid for arbitrary correlation lag. For time-dependent processes, it requires the limit of vanishing lag. These bounds hold true for any system that follows either a Markovian dynamics or a coupled set of overdamped Langevin equations on some underlying, unobservable level of description. We illustrate the bounds for both types of dynamics and discuss their optimization and potential tightness.

cond-mat.stat-mech↗

arXiv2026

Compensating random transition-detection blackouts in Markov networks

In Markov networks, measurement blackouts with unknown frequency compromise observations such that thermodynamic quantities can no longer be inferred reliably. In particular, the observed currents neither discern equilibrium from non-equilibrium nor can they be used in extant estimators of entropy production. Our strategy to eliminate these effects is based on formally attributing the blackouts to a second channel connecting states. The unknown frequency of blackouts and the true underlying transition rates can be determined from the short-time limit of observed waiting-time distributions. A post-modification of observed trajectory data yields a virtual effective dynamics from which the lower bound on entropy production based on thermodynamic uncertainty relations can be recovered fully. Moreover, the post-processed data can be used in waiting-time based estimators. Crucially, our strategy does not require the blackouts to occur homogeneously or symmetrically under time-reversal.

cond-mat.stat-mech↗

arXiv2025

A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production

Semi-Markov processes play an important role in the effective description of partially accessible systems in stochastic thermodynamics. They occur, for instance, in coarse-graining procedures such as state lumping and when analyzing waiting times between few visible Markovian events. The finite-time measurement of any coarse-grained observable in a stochastic system depends on the specific realization of the underlying trajectory. Moreover, the fluctuations of such observables are encoded in their rate function that follows from the rate function of the empirical measure and the empirical flow in the respective process. Derivations of the rate function of empirical measure and empirical flow in semi-Markov processes with direction-time independence (DTI) exist in the mathematical literature, but have not received much attention in the stochastic thermodynamics community. We present an accessible derivation of the rate function of the tuple frequency in discrete-time Markov chains and extend this to the rate function of the empirical semi-Markov kernel in semi-Markov processes without DTI. From this, we derive an upper bound on the rate function of the empirical entropy production rate, which leads to a lower bound on the variance of the mean entropy production rate measured along a finite-time trajectory. We illustrate these analytical bounds with simulated data.

cond-mat.stat-mech↗

arXiv2025

From observed transitions to hidden paths in Markov networks

The number of observable degrees of freedom is typically limited in experiments. Here, we consider discrete Markov networks in which an observer has access to a few visible transitions and the waiting times between these transitions. Focusing on the underlying structure of a discrete network, we present methods to infer local and global properties of the network from observed data. First, we derive bounds on the microscopic entropy production along the hidden paths between two visible transitions, which complement extant bounds on mean entropy production and affinities of hidden cycles. Second, we demonstrate how the operationally accessible data encodes information about the topology of shortest hidden paths, which can be used to identify potential clusters of states or exclude their existence. Finally, we outline a systematic way to combine the inferred data, resulting in an algorithm that finds the candidates for a minimal graph of the underlying network, i.e., a graph that is part of the original one and compatible with the observations. Our results highlight the interplay between thermodynamic methods, waiting-time distributions and topological aspects like network structure, which can be expected to provide novel insights in other set-ups of coarse graining as well.

cond-mat.stat-mech↗

arXiv2024

Inferring kinetics and entropy production from observable transitions in partially accessible, periodically driven Markov networks

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the periodic probabilities of states connected by these observed transitions and their time-dependent transition rates can be inferred. Moreover, the smallest number of hidden transitions between accessible ones and some of their transition rates can be extracted. We prove and conjecture lower bounds on the total entropy production for such periodic stationary states. Even though our techniques are based on generalizations of known methods for steady states, we obtain original results for those as well.

cond-mat.stat-mech↗