## What is/are Stochastic Thermodynamics?

Stochastic Thermodynamics - In particular, the theoretical model allows us to define fluctuating currents and to study the stochastic thermodynamics of the system, with focus on the distribution of the extracted work over different time intervals.^{[1]}Understanding the connections between information and thermodynamics has been among the most visible applications of stochastic thermodynamics.

^{[2]}The upper bound is related to recent generalizations of linear response relations in Stochastic Thermodynamics, and shares common features with Fisher’s fundamental theorem of natural selection, and with its generalization by Price, although they define different measures of selection.

^{[3]}We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation.

^{[4]}Within the framework of stochastic thermodynamics, and for models of thermodynamic engines in the idealized case of underdamped particles in the low-friction regime, we derive explicit bounds as well as optimal control protocols that draw maximum power and achieve maximum efficiency at any specified level of power.

^{[5]}Developments pivoting around the frameworks of stochastic thermodynamics, open quantum systems, and quantum information theory have led to substantial progress in such endeavour.

^{[6]}In order to tackle this, we exploit the recently postulated Least microEnvironmental Uncertainty Principle (LEUP) to develop a theory of stochastic thermodynamics for cell differentiation.

^{[7]}Markov blankets, information geometry and stochastic thermodynamics.

^{[8]}Inspired by recent developments in stochastic thermodynamics, we implemented a data-driven and model-free deep learning framework to decode the temporal inversion of electrocorticography signals acquired from non-human primates.

^{[9]}One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role.

^{[10]}This demonstrates that recent concepts of stochastic thermodynamics used to study micro-systems subject to thermal fluctuations can further the understanding of geophysical fluid dynamics with turbulent fluctuations.

^{[11]}In this work, we generalize the standard Stuart–Landau dimer model to include effects due to an inertia-like term and noise and study its dynamics and stochastic thermodynamics.

^{[12]}Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics and stochastic thermodynamics.

^{[13]}Going beyond rate-equation dynamics is not only possible, but necessary if stochastic thermodynamics is to become part of the paradigm for physical information processing.

^{[14]}Distinct optimization protocols are analyzed in the framework of stochastic thermodynamics.

^{[15]}By utilizing the concepts in stochastic thermodynamics and graph theory analysis, the Clausius and nonequilibrium free energy inequalities are built to interpret the local second law of thermodynamics for subsystems.

^{[16]}We study the relation between stochastic thermodynamics and nonequilibrium thermodynamics by evaluating the entropy production and the relation between fluxes and forces in a harmonic system with N particles in contact with N different reservoirs.

^{[17]}Recent developments in stochastic thermodynamics have shown that fluctuations in many far-from-equilibrium systems are constrained by the rate of entropy production via so-called thermodynamic uncertainty relations.

^{[18]}We introduce a thermodynamically consistent model for a discrete time crystal and analyze it using the framework of stochastic thermodynamics.

^{[19]}This demonstrates that recent concepts of stochastic thermodynamics used to study micro-systems subject to thermal fluctuations can further the understanding of geophysical fluid dynamics with turbulent fluctuations.

^{[20]}In the quasistatic limit, the formula for T_{eff}(t) simplifies and coincides with a recently proposed temperature for stochastic thermodynamics, bearing a compact expression for the maximum efficiency.

^{[21]}Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.

^{[22]}The maximum amount of work that can be extracted in a single measurement and the corresponding feedback loop is given by the information that is acquired via the measurement, a result that manifests the close relation between information theory and stochastic thermodynamics.

^{[23]}The common saying, that information is power, takes a rigorous form in stochastic thermodynamics, where a quantitative equivalence between the two helps explain the paradox of Maxwell’s demon in its ability to reduce entropy.

^{[24]}This is the first step towards studying colloidal particles in dynamically modulated optical potentials to explore the stochastic thermodynamics of mesoscopic systems and small-scale thermo-mechanical machines.

^{[25]}In order to tackle this, we exploit the recently postulated Least microEnvironmental Uncertainty Principle (LEUP) to develop a theory of stochastic thermodynamics for cell differentiation.

^{[26]}Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics, and stochastic thermodynamics.

^{[27]}Approaches in information theory and stochastic thermodynamics can explain how pathway selections are processed from environmental stimuli.

^{[28]}Our work bridges the gap between the engineering of low dissipation digital devices and theoretical developments in stochastic thermodynamics, and provides a platform to study design principles for low dissipation digital devices.

^{[29]}Within the framework of stochastic thermodynamics, and for models of thermodynamic engines in the idealized case of underdamped particles in the low-friction regime subject to a harmonic potential, we derive explicit bounds as well as optimal control protocols that draw maximum power and achieve maximum efficiency at any specified level of power.

^{[30]}Despite recent progress through techniques such as computer simulations, large deviation theory, and stochastic thermodynamics (e.

^{[31]}Stochastic thermodynamics is a recently introduced approach to deals with small systems in contact with one or more thermal baths.

^{[32]}Such systems are captured within the framework of stochastic thermodynamics, which describes the fluctuating thermodynamic quantities of driven systems.

^{[33]}In this paper, motivated by a general interest in the stochastic thermodynamics of small systems, we derive an exact expression-via path integrals-for the conditional probability density of a two-dimensional harmonically confined Brownian particle acted on by linear mixed flow.

^{[34]}We discuss similarities and differences with the rate function of the efficiency in stochastic thermodynamics.

^{[35]}This paper proposes new avenues for origins research that apply modern concepts from stochastic thermodynamics, information thermodynamics and complexity science.

^{[36]}Crucially, this means that there is an explicit link between the inference performed by internal states and their energetics—as characterized by their stochastic thermodynamics.

^{[37]}We combine techniques from algorithmic information theory and stochastic thermodynamics to analyze the thermodynamic costs of TMs.

^{[38]}We propose a generalization of stochastic thermodynamics to systems of active particles, which move under the combined influence of stochastic internal self-propulsions (activity) and a heat bath.

^{[39]}In particular, we use the apparatus of stochastic thermodynamics to investigate the role of noise and thermodynamic cost in feedback-driven oscillations.

^{[40]}We perform an analytic study on the stochastic thermodynamics of a small classical particle trapped in a time-dependent single-well potential in the highly underdamped limit.

^{[41]}The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale.

^{[42]}By introducing elements of stochastic thermodynamics, we analyze the information flow and associated entropy production during gating cycle of a single channel.

^{[43]}A cost-precision trade-off relationship, the so-called thermodynamic uncertainty relation (TUR), has been recently discovered in stochastic thermodynamics.

^{[44]}Sagawa and Ueda established a fluctuation theorem of information exchange by revealing the role of correlations in stochastic thermodynamics and unified the non-equilibrium thermodynamics of measurement and feedback control.

^{[45]}We extend the theory of stochastic thermodynamics in three directions: (i) instead of a continuously monitored system we consider measurements only at an arbitrary set of discrete times, (ii) we allow for imperfect measurements and incomplete information in the description, and (iii) we treat arbitrary manipulations (e.

^{[46]}Stochastic thermodynamics is an extension of classical nonequilibrium thermodynamics to small systems, where fluctuations are expected to play an important role.

^{[47]}This paper is a theoretical study of the stochastic thermodynamics of a single, optically trapped particle that is initially in equilibrium at temperature T and is then subjected to a steady 2D extensional flow.

^{[48]}Stochastic thermodynamics is an extension of classical nonequilibrium thermodynamics to small systems, where fluctuations are expected to play an important role.

^{[49]}In this paper I review some of this recent work on the `stochastic thermodynamics of computation'.

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## Quantum Stochastic Thermodynamics

The latter is widely used in the analysis and calculations of stochastic thermodynamic quantities in quantum stochastic thermodynamics.^{[1]}Our work initiates the study of quantum stochastic thermodynamics based on group-representation theory.

^{[2]}We set up a framework for quantum stochastic thermodynamics based solely on experimentally controllable but otherwise arbitrary interventions at discrete times.

^{[3]}Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model.

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## Using Stochastic Thermodynamics

Using stochastic thermodynamics, we take realistic state populations derived from the phonon-assisted dynamics of electron-hole pairs within photoexcited organic bilayers to connect the kinetics with the free energy profile of charge separation.^{[1]}Using stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time-dependent temperature, in which case the systems are permanently out of thermodynamic equilibrium, inducing a continuous generation of entropy.

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## Classical Stochastic Thermodynamics

In the classical limit, the transformations becomes those used in the functional integral formalism of the classical stochastic thermodynamics to derive the classical fluctuation theorem.^{[1]}An important result in classical stochastic thermodynamics is the work fluctuation-dissipation relation (FDR), which states that the dissipated work done along a slow process is proportional to the resulting work fluctuations.

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## stochastic thermodynamics allows

Here we show that modern stochastic thermodynamics allows us to interpret the measurements obtained by friction force microscopy, which is the standard tool for investigating the frictional properties of materials, in terms of basic thermodynamics concepts such as fluctuating work and entropy.^{[1]}Stochastic thermodynamics allows us to define heat and work for microscopic systems far from thermodynamic equilibrium, based on observations of their stochastic dynamics.

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