Entropy Production and Fluctuation Theorems for Active Matter

Abstract

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 generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.

Clausius Relation for Active Particles: What Can We Learn from Fluctuations

“…In [21] a "mass-less" active temperature T τ = D a /τ was defined. In this paper we show that it is not necessary, if an "effective mass" µ = γτ is used, as in [23]. Of course there is no thermostat at temperature T a , such a temperature is only useful to define a relevant energy scale.…”

“…However it is quite difficult to imagine Equation (5) in macroscopic thermodynamics, since the very definition of macroscopic entropy production is the difference between dS and δQ/T [6]. On the contrary, equations similar to (5) have appeared in the literature in a stochastic thermodynamic treatment of systems with feedback and model of self-propelled particles [15][16][17][18]23]. …”

“…The crucial point here is that both such a "coarse-grained heat" and the effective temperature can be measured in experiments and therefore a test of this active Clausius relation can be attempted. In the last year other two proposals have appeared in the literature [22,23], devoted to define entropy production and heat in the same identical model. The purpose of the present paper is to discuss the connection between those different Clausius relations.…”

“…Apart from this comparison, two novelties are present here with respect to [21]: (1) a single trajectory level of description is adopted, while in [21] an ensemble average had been considered; (2) a generalization of [21] to more than one dimension and interacting particles is presented. In order to simplify the discussion, the main discussion is focused on the 1d case with a time-independent potential, which is sufficient to show the main difference between the definitions of heat and entropy production in the three works considered [21][22][23]. The generalisation of the proposal in [21] to multi-dimensional cases with a time-dependent potential is also discussed at the end.…”

“…In Section 3, we introduce the active model with Gaussian colored noise with thermal fluctuations, where a "microscopic Clausius relation" is trivially satisfied, and then show what happens at the coarse-grained level, when inertia and thermal fluctuations are neglected. The three recipes appeared in [21][22][23] to connect entropy production, dissipated heat and temperature are reviewed and compared.…”