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

Abstract

Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom-or arbitrariness-appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the original Clausius relation and can be experimentally verified.

Autonomous Engines Driven by Active Matter: Energetics and Design Principles

“…The difference between the effective input P ac and the actual output power P ex leads to the definition of the coarse-grained entropy production Σ ≡ (P ac − P ex )/T . Several recent works quantify irreversibility in active matter in terms of the ratio of forward and backward path probabilities [65,[69][70][71][72][73]. The same entropy production Σ emerges in such a framework by applying the standard principles of stochastic thermodynamics to the joint trajectory of {r i a }, {n i } and r p and considering both {n i } and f ex as even under time reversal.…”

Collective forces in scalar active matter

“…The major conceptual difficulty is that the behavior of the particle orientation under time reversal is not fixed by the model but has to be supplied: either odd (e † i = −e i ) corresponding to interpreting v 0 e i as a solvent velocity or even (e † i = e i ) with (v 0 /µ 0 )e i behaving as a nonconservative (stochastic) force [45,106,107]. Clearly, this choice leads to different expressions for ∆s m [108][109][110][111].…”

Active Ornstein-Uhlenbeck particles

“…This means that the drift term in Eq. (7) for ρ = ρ s has to be the same as the drift term in Eq. (3) under the time reversal transformation: t → −t, x = x, p = −p,…”

“…[5]) and on formulas for the energy and heat transfer. This result was, in turn, declared to be incorrect by Caprini et al, who used a different calculation of entropy production also based on path integral representations [6,7]. Further discussions of entropy calculations, including the convenience to change the model by adding a thermal noise to the AOUPs, are found in Ref.…”