arXiv subjects

Jonas H. Fritz

Publications and source records attributed to Jonas H. Fritz.

5 recordsLinked to original sources

arXiv2026

Waiting-time based entropy estimators in continuous space without Markovian events

Estimating entropy production in continuous systems that can only be observed with a limited resolution remains an open problem in stochastic thermodynamics. Existing estimators based on the measurement of waiting-time distributions require either the detection of Markovian events, which uniquely determine the state of the system, or assume a discrete underlying dynamics. We present a novel estimator that relies solely on the detection of a single particle leaving or entering regions, or crossing manifolds, in continuous space. This estimator is based on the frequency and the duration of transitions between such events. We derive this bound by introducing two kinds of discretization of space. Finally, we compare our novel bound to the thermodynamic uncertainty relation improved by correlations using simulations of a Brownian vortex and discuss its relation to other lower bounds to entropy production.

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

Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics

Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare the performance of three different entropy estimators under these limitations for two different paradigmatic systems, a four-state Markov network and an augmented Michaelis-Menten reaction scheme. We consider the thermodynamic uncertainty relation, a waiting-time based estimator for resolved transitions and a waiting-time based estimator for blurred transitions in imperfect observation scenarios. For perfect measurement statistics and finite temporal resolution, the estimator based on resolved transitions performs best in all considered scenarios. The thermodynamic uncertainty relation gives a better estimate than the estimator based on blurred transitions at low driving affinities, whereas the latter performs better at high driving affinities. Furthermore, we find that a higher temporal and spatial resolution leads to slower convergence of measurement statistics, implying that for short measurement times, a lower resolution may be beneficial. Additionally, we identify a self-averaging effect for the waiting-time based entropy estimators that can reduce their variance for observations with finite statistics.

cond-mat.stat-mech↗

arXiv2023

Thermodynamically consistent model of an active Ornstein-Uhlenbeck particle

Identifying the full entropy production of active particles is a challenging task. We introduce a microscopic, thermodynamically consistent model, which leads to active Ornstein-Uhlenbeck statistics in the continuum limit. Our minimal model consists of a particle with a fluctuating number of active reaction sites which contribute to its active self-propulsion on a lattice. In addition, the model also takes ordinary thermal noise into account. This approach allows us to identify the full entropy production stemming from both thermal diffusion and active driving. Extant methods based on the comparison of forward and time-reversed trajectory underestimate the physical entropy production when applied to the Langevin equations obtained from our model. Constructing microscopic Markovian models can thus provide a benchmark for determining the entropy production in non-Markovian active systems.

cond-mat.stat-mech↗

arXiv2020

Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator

Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady state (NESS). In reality, these processes take place in finite systems containing a finite number of molecules. In such systems, a NESS can be reached with the help of an externally driven pump for which we introduce a simple model. Crucial parameters are the pumping rate and the finite size of the chemical reservoir. We apply this model to a simple biochemical oscillator, the Brusselator, and quantify the performance using the number of coherent oscillations. As a surprising result, we find that higher precision can be achieved with finite-size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.

cond-mat.stat-mech↗