Fluctuations When Driving Between Nonequilibrium Steady States

Abstract

Maintained by environmental fluxes, biological systems are thermodynamic processes that operate far from equilibrium without detailed-balance dynamics. Yet, they often exhibit well defined nonequilibrium steady states (NESSs). More importantly, critical thermodynamic functionality arises directly from transitions among their NESSs, driven by environmental switching. Here, we identify constraints on excess thermodynamic quantities that ride above the NESS housekeeping background. We do this by extending the Crooks fluctuation theorem to transitions among NESSs, without invoking an unphysical dual dynamics. This and corresponding integral fluctuation theorems determine how much work must be expended when controlling systems maintained far from equilibrium. This generalizes feedback control theory, showing that Maxwellian Demons can leverage mesoscopic-state information to take advantage of the excess energetics in NESS transitions. Altogether, these point to universal thermodynamic laws that are immediately applicable to the accessible degrees of freedom within the effective dynamic at any emergent level of hierarchical organization. By way of illustration, this readily allows analyzing a voltage-gated sodium ion channel whose molecular conformational dynamics play a critical functional role in propagating action potentials in mammalian neuronal membranes.

Kibble-Zurek scaling of the irreversible entropy production

“…In such nonequilibrium situations the part of the entropy production that corresponds to the excess work is Σ nad , which vanishes in the limit of quasistatic driving for which p(t) ≡ p ss (t) [49][50][51]53]. In complete analogy to Eq.…”

Unified formalism for entropy production and fluctuation relations

“…For systems with detailed balance, the sum of this fluctuating relative entropy and the free energy defined in classical equilibrium thermodynamics was called nonequilibrium free energy in [54]. For this reason, the relative entropy also got a name nonsteady-state addition (to free energy) in [12]. Furthermore, it was shown in [55] that this relative entropy itself could be understood physically as a "free energy" as well.…”

“…Various distinct FRs for different EPs have been studied in various settings including discrete-time Markov chains [6,[10][11][12], continuous-time Markov chains (Markov jump processes) [13][14][15][16][17][18], diffusion processes (as stochastic differential equations or Langevin equations) [10,[17][18][19][20][21][22], and even general stochastic processes [2,8,17,[23][24][25]. To discuss a few, in [8], Crooks' fluctuation theorem for the total entropy production was introduced for systems with detailed balance and the conditions for it to hold was illustrated; in [23], the dissipation function from Evans and Searles [26] was rigorously shown to generally admit the transient fluctuation theorem (TFT); in [15], a detailed fluctuation theorem related to the involutive property of the change in probability (iDFT) was introduced but the correct condition for total entropy production and non-adiabatic entropy production was not stated; in [3], the generalized Crooks' fluctuation theorem for non-detail balanced systems (rDFT) and TFT for different EPs were discussed thoroughly for diffusion processes.…”

Balancing error and dissipation in computing

“…(27) of Ref. [41], the more general starting point is In steady-state biological processes, there is no external control. The controllable parameters can thus be considered as held constant, such that the driving protocol is trivially time-symmetric R(x 0:τ ) = x 0:τ = x 0 x 0 .…”