A thermodynamic uncertainty relation for a system with memory

We introduce an example of thermodynamic uncertainty relation (TUR) for systems modeled by a one-dimensional generalised Langevin dynamics with memory, determining the motion of a micro-bead driven in a complex fluid. Contrary to TURs typically discussed in the previous years, our observables and the entropy production rate are one-time variables. The bound to the signal-to-noise ratio of such state-dependent observables only in some cases can be mapped to the entropy production rate. For example, this is true in Markovian systems. Hence, the presence of memory in the system complicates the thermodynamic interpretation of the uncertainty relation

Explicit solution of the generalised Langevin equation

Generating an initial condition for a Langevin equation with memory is a non trivial issue.We introduce a generalisation of the Laplace transform as a useful tool for solving thisproblem, in which a limit procedure may send the extension of memory effects to arbitrarytimes in the past. This method allows us to compute average position, work, their variancesand the entropy production rate of a particle dragged in a complex fluid by an harmonicpotential, which could represent the effect of moving optical tweezers. For initial conditionsin equilibrium we generalise the results by van Zon and Cohen, finding the variance of thework for generic protocols of the trap. In addition, we study a particle dragged for a longtime captured in an optical trap with constant velocity in a steady state. Our formulas openthe door to thermodynamic uncertainty relations in systems with memory

Off-label long acting injectable antipsychotics in real-world clinical practice: a cross-sectional analysis of prescriptive patterns from the STAR Network DEPOT study

Introduction Information on the off-label use of Long-Acting Injectable (LAI) antipsychotics in the real world is lacking. In this study, we aimed to identify the sociodemographic and clinical features of patients treated with on- vs off-label LAIs and predictors of off-label First- or Second-Generation Antipsychotic (FGA vs. SGA) LAI choice in everyday clinical practice. Method In a naturalistic national cohort of 449 patients who initiated LAI treatment in the STAR Network Depot Study, two groups were identified based on off- or on-label prescriptions. A multivariate logistic regression analysis was used to test several clinically relevant variables and identify those associated with the choice of FGA vs SGA prescription in the off-label group. Results SGA LAIs were more commonly prescribed in everyday practice, without significant differences in their on- and off-label use. Approximately 1 in 4 patients received an off-label prescription. In the off-label group, the most frequent diagnoses were bipolar disorder (67.5%) or any personality disorder (23.7%). FGA vs SGA LAI choice was significantly associated with BPRS thought disorder (OR = 1.22, CI95% 1.04 to 1.43, p = 0.015) and hostility/suspiciousness (OR = 0.83, CI95% 0.71 to 0.97, p = 0.017) dimensions. The likelihood of receiving an SGA LAI grew steadily with the increase of the BPRS thought disturbance score. Conversely, a preference towards prescribing an FGA was observed with higher scores at the BPRS hostility/suspiciousness subscale. Conclusion Our study is the first to identify predictors of FGA vs SGA choice in patients treated with off-label LAI antipsychotics. Demographic characteristics, i.e. age, sex, and substance/alcohol use co-morbidities did not appear to influence the choice towards FGAs or SGAs. Despite a lack of evidence, clinicians tend to favour FGA over SGA LAIs in bipolar or personality disorder patients with relevant hostility. Further research is needed to evaluate treatment adherence and clinical effectiveness of these prescriptive patterns

The Role of Attitudes Toward Medication and Treatment Adherence in the Clinical Response to LAIs: Findings From the STAR Network Depot Study

Background: Long-acting injectable (LAI) antipsychotics are efficacious in managing psychotic symptoms in people affected by severe mental disorders, such as schizophrenia and bipolar disorder. The present study aimed to investigate whether attitude toward treatment and treatment adherence represent predictors of symptoms changes over time. Methods: The STAR Network \u201cDepot Study\u201d was a naturalistic, multicenter, observational, prospective study that enrolled people initiating a LAI without restrictions on diagnosis, clinical severity or setting. Participants from 32 Italian centers were assessed at three time points: baseline, 6-month, and 12-month follow-up. Psychopathological symptoms, attitude toward medication and treatment adherence were measured using the Brief Psychiatric Rating Scale (BPRS), the Drug Attitude Inventory (DAI-10) and the Kemp's 7-point scale, respectively. Linear mixed-effects models were used to evaluate whether attitude toward medication and treatment adherence independently predicted symptoms changes over time. Analyses were conducted on the overall sample and then stratified according to the baseline severity (BPRS < 41 or BPRS 65 41). Results: We included 461 participants of which 276 were males. The majority of participants had received a primary diagnosis of a schizophrenia spectrum disorder (71.80%) and initiated a treatment with a second-generation LAI (69.63%). BPRS, DAI-10, and Kemp's scale scores improved over time. Six linear regressions\u2014conducted considering the outcome and predictors at baseline, 6-month, and 12-month follow-up independently\u2014showed that both DAI-10 and Kemp's scale negatively associated with BPRS scores at the three considered time points. Linear mixed-effects models conducted on the overall sample did not show any significant association between attitude toward medication or treatment adherence and changes in psychiatric symptoms over time. However, after stratification according to baseline severity, we found that both DAI-10 and Kemp's scale negatively predicted changes in BPRS scores at 12-month follow-up regardless of baseline severity. The association at 6-month follow-up was confirmed only in the group with moderate or severe symptoms at baseline. Conclusion: Our findings corroborate the importance of improving the quality of relationship between clinicians and patients. Shared decision making and thorough discussions about benefits and side effects may improve the outcome in patients with severe mental disorders

Il ruolo della varianza in sistemi stocastici classici

We characterise stochastic systems by studying their variances. In particular, we tackle this topic from two points of view, by elaborating on the subject of stochastic uncertainty relations and by discussing a novel result that we term the variance sum rule for Langevin systems. Stochastic uncertainty relations are inequalities that usually involve a signal to noise ratio g, which can be regarded as a measure of the precision associated to the observable O, and a cost function C such that g ≤ C. The thermodynamic uncertainty relation is one of the first examples of these stochastic inequalities and considers the average total entropy production in the cost function, thus refining the second law of thermodynamics. By means of an information-theoretic approach, we provide a new uncertainty relation for a system modelled by a linear generalised Langevin equation along with a novel kinetic uncertainty relation, where the upper bound to the precision is given by the mean dynamical activity, which quantifies the degree of agitation of a discrete system. We also show how the latter is often the main limiting factor for the precision in far-from-equilibrium conditions. In the second part of the thesis we introduce some variance sum rules, which can be used to infer relevant dynamical parameters also for regimes far from equilibrium. We test our method on experimental data whose model parameters are known a priori, finding very good agreement between the results of the estimation procedure and the true values of the parameters. A specific sum rule for non-Markovian systems also shows good performances in estimating the memory kernel of complex fluids. Moreover, the same approach yields a solid formula for estimating the amount of entropy production. All of this shows that the indetermination of stochastic motion is a resource that we should continue to understand and exploit for measuring physical quantities.We characterise stochastic systems by studying their variances. In particular, we tackle this topic from two points of view, by elaborating on the subject of stochastic uncertainty relations and by discussing a novel result that we term the variance sum rule for Langevin systems. Stochastic uncertainty relations are inequalities that usually involve a signal to noise ratio g, which can be regarded as a measure of the precision associated to the observable O, and a cost function C such that g ≤ C. The thermodynamic uncertainty relation is one of the first examples of these stochastic inequalities and considers the average total entropy production in the cost function, thus refining the second law of thermodynamics. By means of an information-theoretic approach, we provide a new uncertainty relation for a system modelled by a linear generalised Langevin equation along with a novel kinetic uncertainty relation, where the upper bound to the precision is given by the mean dynamical activity, which quantifies the degree of agitation of a discrete system. We also show how the latter is often the main limiting factor for the precision in far-from-equilibrium conditions. In the second part of the thesis we introduce some variance sum rules, which can be used to infer relevant dynamical parameters also for regimes far from equilibrium. We test our method on experimental data whose model parameters are known a priori, finding very good agreement between the results of the estimation procedure and the true values of the parameters. A specific sum rule for non-Markovian systems also shows good performances in estimating the memory kernel of complex fluids. Moreover, the same approach yields a solid formula for estimating the amount of entropy production. All of this shows that the indetermination of stochastic motion is a resource that we should continue to understand and exploit for measuring physical quantities

Thermodynamic uncertainty relation

The starting point of my thesis is a recent result of microscopic thermodynamics obtained with techniques related to linear response theory. The theorem in question, pictorially called thermodynamic uncertainty principle, forms part of the more general framework of thermodynamic inequalities, which arise from the handling of microscopic processes in a non-equilibrium state. More specifically, the above-mentioned theorem puts a bound on the ratio between the average rate of the an out of equilibrium current and the generalized diffusivity (proportional to the variance of the current) times the entropy production rate. However, it was showed that this thermodynamic relation can be obtained in a more general way, namely using a mathematical object called the Kullback-Leibler divergence that in some particular cases can be linked to entropy production. Hence, in this thesis, we use the latter to obtain general non-equilibrium inequalities for systems modelled by continuous time Markov chains and for some specific Langevin systems, not necessarily aiming to recover the thermodynamic uncertainty relation. In fact, performing some simpler perturbations on the system's dynamic and using linear response theory we calculate the Kullback-Leibler divergences that arise from this procedure and we will relate the obtained results to other relevant observables of the system which will not necessarily be entropy production . This will be done in particular for general jump processes where we perform a linear perturbation of the transition rates obtaining a relation between the variance of a given observable, the time derivative of its mean and the activity of the system, namely the average total number of jumps that the system performed up to time T. We will also discuss general Brownian motion with memory effects and time dependent external force, the results we obtain involve the variance of a given observable, its susceptibility to the performed perturbation and of course the Kullback-Leibler divergence that we believe, in this particular situation, to be linked to the dissipation of the system as the perturbations we use involves the friction kernel of the Langevin equation used to model the system in question. Moreover, using position as observable in the obtained inequalities and plotting the saturation ratio for these we will get interesting informations about the dominant components (deterministic or random) of the dynamics at different times

Kinetic uncertainty relation

Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is fundamentally different from the thermodynamic uncertainty relation recently discussed in the literature. The thermodynamic constraint is more relevant close to equilibrium while the kinetic constraint is the limiting factor of the precision of a observables in regimes far from equilibrium. This is visualized for paradigmatic simple systems and with an example of molecular motor dynamics. Our approach is based on the recent fluctuation response inequality by Dechant and Sasa (2018 arXiv:1804.08250) and can be applied to generic Markov jump systems, which describe a wide class of phenomena and observables, including the irreversible predator-prey dynamics that we use as an illustration

Variance sum rule: proofs and solvable models

We derive, in more general conditions, a recently introduced variance sum rule (VSR) (Di Terlizzi et al 2024 Science 383 971) involving variances of displacement and force impulse for overdamped Langevin systems in a nonequilibrium steady state (NESS). This formula allows visualising the effect of nonequilibrium as a deviation of the sum of variances from normal diffusion 2 Dt , with D the diffusion constant and t the time. From the VSR, we also derive formulas for the entropy production rate σ that, differently from previous results, involve second-order time derivatives of position correlation functions. This novel feature gives a criterion for discriminating strong nonequilibrium regimes without measuring forces. We then apply and discuss our results to three analytically solved models: a stochastic switching trap, a Brownian vortex, and a Brownian gyrator. Finally, we compare the advantages and limitations of known and novel formulas for σ in an overdamped NESS