A run-and-tumble particle in a one dimensional box (infinite potential well) is studied. The steady state is analytically solved and analyzed, revealing the emergent length scale of the boundary layer where particles accumulate near the walls. The mesoscopic steady state entropy production rate of the system is derived from coupled Fokker-Planck equations with a linear reaction term, resulting in an exact analytic expression. The entropy production density is shown to peak at the walls. Additionally, the derivative of the entropy production rate peaks at a system size proportional to the length scale of the accumulation boundary layer, suggesting that the behavior of the entropy production rate and its derivatives as a function of the control parameter may signify a qualitative behavior change in the physics of active systems, such as phase transitions.
Entropy production of an active particle in an external potential is identified through a thermodynamically consistent minimal lattice model that includes the chemical reaction providing the propulsion and ordinary translational noise. In the continuum limit, a unique expression follows, comprising a direct contribution from the active process and an indirect contribution from ordinary diffusive motion. From the corresponding Langevin equation, this physical entropy production cannot be inferred through the conventional, yet here ambiguous, comparison of forward and time-reversed trajectories.…
Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a gene…
We consider a colloidal particle immersed in an active bath and derive a Smoluchowski equation that governs the dynamics of colloidal particle. We address this as active Smoluchowski equation. Our analysis based on this active Smoluchowski equation shows a short time superdiffusive behavior that strongly depends on the activity. Our model also predicts a non-monotonic dependence of mean energy dissipation against time, a signature of activity-induced dynamics. By introducing a frequency-dependent effective temperature, we show that the mean rate of entropy production is time dependent unlike a…
In active $φ^4$ field theories the nonequilibrium terms play an important role in describing active phase separation; however, they are irrelevant, in the renormalization group sense, at the critical point. Their irrelevance makes the critical exponents the same as those of the Ising universality class. Despite their irrelevance, they contribute to a nontrivial scaling of the entropy production rate at criticality. We consider the nonequilibrium dynamics of a nonconserved scalar field $φ$ (Model A) driven out-of-equilibrium by a persistent noise that is correlated on a finite timescale $τ$, as…
Recently, the fundamental laws of thermodynamics have been reconsidered for small systems. The discovery of the fluctuation relations has spurred theoretical and experimental studies on thermodynamics of systems with few degrees of freedom. The concept of entropy production has been extended to the microscopic level by considering stochastic trajectories of a system coupled to a heat bath. However, the experimental observation of the microscopic entropy production remains elusive. We measure distributions of the microscopic entropy production in a single-electron box consisting of two islands …
It is currently a widely used practice to write the constraints in terms of escort averages when the generalized entropies are employed in the maximization scheme. We show that the maximization of the nonadditive $q$-entropy with escort averages leads either to an overall lack of connection with thermodynamics or violation of the second and third laws of thermodynamics if one adopts the Clausius definition of the physical temperature. If an alternative definition of physical temperature is chosen by respecting the divisibility of the total system into independent subsystems, thermodynamic rela…
Collections of self-propelled particles that move persistently by continuously consuming free energy are a paradigmatic example of active matter. In these systems, unlike Brownian "hot colloids", the breakdown of detailed balance yields a continuous production of entropy at steady state, even for an ideal active gas. We quantify the irreversibility for a non-interacting active particle in two dimensions by treating both conjugated and time-reversed dynamics. By starting with underdamped dynamics, we identify a hidden rate of entropy production required to maintain persistence and prevent the r…
Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom has remained of little practical significance because the high-dimensionality of their state space makes it difficult to measure. Here we introduce a local measure of entropy production and a numerical protocol to estimate it. We establish a connection between the entropy production and extractability of work in a given region of the system and show how this q…
Recent studies of nonequilibrium phase transitions have shown that in many systems which have transitions involving an arrested phase, the arrested states show suppressed density fluctuations and a cusp in the configurational entropy at the transition point. We study quasistatic driving in the 1D fixed-energy abelian sandpile model, and in conserved lattice gases with range $n$ in 1D, and exactly determine the measure over the absorbing states for both cases, along with the behaviour of density fluctuations and the configurational entropy of absorbing states. We show that both models exhibit h…
We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particle…
Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: it vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles witho…
We propose a minimal model, based on active Brownian particles, for the dynamics of cells confined in a two-state micropattern, composed of two rectangular boxes connected by a bridge, and investigate the transition statistics. A transition between boxes occurs when the active particle crosses the center of the bridge, and the time between subsequent transitions is the dwell time. By assuming that the rotational diffusion time $τ$ is a function of the position, the main features of the transition statistics observed experimentally are recovered. $τ$ controls the transition from a ballistic reg…
Active systems are characterized by a continuous production of entropy at steady state. We study the statistics of entropy production within a lattice-based model of interacting active particles that is capable of motility-induced phase separation. Exploiting a recent formulation of the exact fluctuating hydrodynamics for this model, we provide analytical results for its entropy production statistics in both typical and atypical (biased) regimes. This complements previous studies of the large deviation statistics of entropy production in off-lattice active particle models that could only be ad…
The present work investigates the effect of inertia on the entropy production rate $Π$ for all canonical models of active particles for different dimensions and the type of confinement. To calculate $Π$, the link between the entropy production and dissipation of heat rate is explored resulting in a simple and intuitive expression. By analyzing the Kramers equation, alternative formulations of $Π$ are obtained and the virial theorem for active particles is derived. Exact results are obtained for particles in an unconfined environment and in a harmonic trap. In both cases, $Π$ is independent of …
Understanding stochastic thermodynamics of active Brownian particles (ABPs) system has been an important topic in very recent years. In this article we study a general model of active Brownian particle systems by introducing a coarse-grained Fokker-Planck equation, which allows us to identify an effective entropy production along a stochastic trajectory, wherein an activity and configuration dependent diffusion coefficient comes into play with an important role. Although the hidden component between the true entropy production and the effective one is dominant, the effective entropy production…
By employing a path integral formulation, we obtain the entropy production rate for a system of active Ornstein-Uhlenbeck particles (AOUP) both in the presence and in the absence of thermal noise. The present treatment clarifies some contraddictions concerning the definition of the entropy production rate in the AOUP model, recently appeared in the literature. We derive explicit formulas for three different cases: overdamped Brownian particle, AOUP with and without thermal noise. In addition, we show that it is not necessary to introduce additional hypotheses concerning the parity of auxiliary…
The approach of an ideal gas to equilibrium is simulated through a generalization of the Ehrenfest ball-and-box model. In the present model, the interior of each box is discretized, {\it i.e.}, balls/particles live in cells whose occupation can be either multiple or single. Moreover, particles occasionally undergo random, but elastic, collisions between each other and against the container walls. I show, both analitically and numerically, that the number and energy of particles in a given box eventually evolve to an equilibrium distribution $W$ which, depending on cell occupations, is binomial…
We address the steady-state entropy production rate (EPR) of active scalar $ϕ^4$ theories, which lack time-reversal symmetry, close to a phase-separation critical point. We consider both nonconserved (Model A) and conserved (Model B) dynamics at Gaussian level, and also address the former at leading order in $ε= 4-d$. In each case, activity is irrelevant in the RG sense: the active model lies in the same (dynamic Ising) universality class as its time-reversible counterpart. Hence one might expect that activity brings no new critical behavior. Here we show instead that the EPR per spacetime cor…
The persistent character of the motion of active particles gives rise to accumulation at boundaries. I investigate the problem of run-and-tumble swimmers confined in a 1D box with hard walls, reporting expressions for the particles probability distribution and wall pressure. A crossover box length value is found below which the initial value of the pressure turns out to be higher than the asymptotic one, indicating a bounce effect of the active "wave" of swimmers. The case of attracting and repelling boundaries are also investigated using two different tumble rates for particles in the bulk an…
Within the Rayleigh-Helmholtz model of active Brownian particles activity is due to a non-linear velocity dependent force. In the presence of an external trapping potential or a constant force, the steady state of the system breaks detailed balance producing a net entropy. Using molecular dynamics simulations, we obtain the probability distributions of entropy production in these steady states. The distribution functions obey detailed fluctuation theorem for entropy production. Using simulation results, we further show that the steady state response function obeys a modified fluctuation-dissip…
Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for total entropy production in such systems using the Fokker-Planck equation. The result is consistent with the expression for stochastic entropy production in the reservoir, that we obtain from probabilities of time-forward and time-reversed trajectories, leading to fluctuation theorems. Numerical simulation is used to find probability distribution of entropy …
In this work we consider information-theoretical observables to analyze short symbolic sequences, comprising time-series that represent the orientation of a single spin in a $2D$ Ising ferromagnet on a square lattice of size $L^2=128^2$, for different system temperatures $T$. The latter were chosen from an interval enclosing the critical point $T_{\rm c}$ of the model. At small temperatures the sequences are thus very regular, at high temperatures they are maximally random. In the vicinity of the critical point, nontrivial, long-range correlations appear. Here, we implement estimators for the …
A colloidal particle immersed in a bath of bacteria is a typical example of a passive particle in an active bath. To model this, we take an overdamped harmonically trapped particle subjected to a thermal and a non-equilibrium noise arising from the active bath. The harmonic well can be attributed to a laser trap or to the small amplitude motion of the sedimented colloid at the bottom of the capillary. In the long time, the system reaches a non-equilibrium steady state that can be described by an effective temperature. By adopting this notion of effective temperature, we investigate whether flu…
We introduce lower bounds for the rate of entropy production of an active stochastic process by quantifying the irreversibility of stochastic traces obtained from mesoscopic degrees of freedom. Our measures of irreversibility reveal signatures of time's arrow and provide bounds for entropy production even in the case of active fluctuations that have no drift. We apply these irreversibility measures to experimental recordings of spontaneous hair-bundle oscillations in mechanosensory hair cells from the ear of the bullfrog. By analysing the fluctuations of only the tip position of hair bundles, …
We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches for the first time a given state. Our main results are: (i) the distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find the exact expressions for the passage probabilities of entropy produ…
Entropy production plays a fundamental role in the study of non-equilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. It was hitherto unknown how the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution. This relationship is of particular relevance to coarse grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under…
Active matter is rapidly becoming a key paradigm of out-of-equilibrium soft matter exhibiting complex collective phenomena, yet the thermodynamics of such systems remain poorly understood. In this letter we study the nonequilbrium thermodynamics of large scale active systems capable of mobility-induced phase separation and polar alignment, using a fully under-damped model which exhibits hidden entropy productions not previously reported in the literature. We quantify steady state entropy production at each point in the phase diagram, revealing characteristic dissipation rates associated with t…
We investigate the informational aspect of (1+1)-dimensional directed percolation, a canonical model of a nonequilibrium continuous transition to a phase dominated by a single special state called the "absorbing" state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of directed percolation. We find a universal relaxation of Renyi entropy at the absorbing phase transition point as well as a new singularity in the active phase, slightly but distinctly away from the absorbing transition point. At the new singular point, the second-orde…
The hydrodynamic equations of dry active polar fluids (i.e., moving flocks without momentum conservation) are shown to imply giant number fluctuations. Specifically, the rms fluctuations $\sqrt {<(δN)^2>}$ of the number $N$ of active particles in a region containing a mean number of active particles $<N>$ scales according to the law $\sqrt {<(δN)^2>} = K'<N>^{ϕ(d)}$ with $ϕ(d)=\frac{7}{10}+\frac{1}{5d}$ in $d\le4$ spatial dimensions. This is much larger the "law of large numbers" scaling $\sqrt {<(δN)^2>} = K\sqrt{<N>}$ found in most equilibrium and non-equilibrium systems. In further contrast…
The relativistic transformation rule for temperature is a subject under debate for more than 110 years. Several incompatible proposals exist in the literature, but a final resolution is still missing. In this work, we reconsider the problem of relativistic transformation rules for a number of thermodynamic parameters, including temperature, chemical potential, pressure, entropy and enthalpy densities for a relativistic perfect fluid using relativistic kinetic theory. The analysis is carried out in a fully relativistic covariant manner, and the explicit transformation rules for the above quanti…
