Mechanical inhibition of dissipation in a thermodynamically consistent active solid

TL;DR

We address how mechano-chemical coupling in dense active solids governs dissipation. We develop a thermodynamically consistent active solid (TCAS) built from active elastic elements whose internal cycles obey local detailed balance and couple to inter-bead stretches via a non-separable energy term, enabling nontrivial cross-talk. Using adiabatic reduction and coarse-graining to a single-dimer picture, we show that the rate of entropy production $\dot{\sigma}$ is non-monotonic in external force $F$ and can be inhibited at large stresses, effectively rendering the material passive; the average elastic energy increases under compression when driving is present. The results reconcile thermodynamic consistency with mechanically induced dissipation modulation and align with measurements in actomyosin networks and crowded condensates, offering a framework for designing smart mechanosensitive materials and thermodynamically consistent active polymers.

Abstract

The study of active solids offers a window into the mechanics and thermodynamics of dense living matter. A key aspect of the non-equilibrium dynamics of such active systems is a mechanistic description of how the underlying mechano-chemical couplings arise, which cannot be resolved in models that are phenomenologically constructed. Here, we follow a bottom-up theoretical approach to develop a thermodynamically consistent active solid (TCAS) model, and uncover a non-trivial cross-talk that naturally ensues between mechanical response and dissipation. In particular, we show that dissipation reaches a maximum at finite stresses, while it is inhibited under large stresses, effectively reverting the system to a passive state. Our findings establish a generic mechanism plausibly responsible for the non-monotonic behaviour observed in recent experimental measurements of entropy production rate in an actomyosin material and enzymatic activity in crowded condensates.

Figures (4)

• Figure 1: The mechanical response to externally applied forces in a broad class of living materials can be represented by the "active spring" model introduced in this work. Examples include DNA tethers extruded by ATP-driven cohesin davidson2019dna, cross-linked bio-polymer networks (active gels prost2015active) and membrane-embedded enzymes Illien2017NovAgudoCanalejo2021chatzittofi2025Chatzittofi2025a or active mechano-sensitive channels Bonthuis2014. These applications are further discussed in suppmat.
• Figure 2: Effect of an external force on a single active elastic element, for $\beta k \bar{\ell}^2=1$ and $U_\ell(\gamma)=0$ for all $\gamma$. In each case, we compare equilibrium ($\Delta\mu=0$, dotted curves) and driven (solid curves) cases: (a) Steady-state probability of the internal state, $\pi_\gamma$, for $\mathbb{L}=\{\bar{\ell},2\bar{\ell},3\bar{\ell}\}$. At equilibrium, the internal state corresponding to the shortest (longest) rest length is generically enhanced under compression (stretching), while driving leads to a repopulation of less energetically favourable states; (b) Entropy production $\dot\sigma$ as a function of $F$ for different choice of the accessible rest lengths $\mathbb{L}$. As $F\to \infty$, dissipation reaches a plateau, due to hard core repulsion preventing the inter-particle distance from decreasing below zero; (c) Average elastic energy stored in the active elastic element.
• Figure 3: Active elastic elements assembled into a one-dimensional bead-spring chain constitute a TCAS. The inter-particle displacement is controlled by a combination of thermal noise, hard-core repulsion and elastic forces, the latter evolving in time according to the dynamics of the internal chemical state of the springs. A representative realisation of the dynamics is shown, with the area between the trajectories of neighbouring beads (solid black lines) colour-coded according to the instantaneous internal state of the spring.
• Figure 4: Mechanical inhibition of dissipation in a TCAS: (a) average entropy production per bead as a function of the dimensionless bead density $\rho = N\bar{\ell}/R$, controlled by varying the ring size $R$ at fixed $N$, for different values of the elastic constant $k$. Here, we take $\beta \Delta\mu=10$, $\mu_{\rm p}=0.01\beta k_m\bar{\ell}^2$, $\beta \epsilon=1$, $\ell_A = 0.9\,\bar{\ell}$, $\ell_B=\bar{\ell}$ and $\ell_C=1.1\,\bar{\ell}$. The length scale associated with the WCA potential is set to $a=0.1\,\bar{\ell}$. The horizontal dashed line corresponds to $\dot{\sigma}_{\rm tot}/N = \frac{1}{3} \beta\Delta\mu \sinh(\beta\Delta\mu/6)$, as obtained from Eq. \ref{['eq:detailedBalance_single']} with $\Delta U_{\gamma\delta} =0$ for all pairs $\gamma,\delta \in \mathbb{L}$; (b) average entropy production as a function of the effective dimensionless pressure suppmat; (c) average conditional current in the dissipative cycle of a given active spring (see suppmat for definitions) as a function of the associated spring length $L_i$ for $N=64$ and $R=64\,\bar{\ell}$ [all other parameters as in (a)]. Solid curves indicate the analytical expression suppmat.