Experimental evidence of detailed balance in granular systems

TL;DR

This paper provides experimental evidence that the principle of detailed balance, traditionally associated with equilibrium systems, can also be satisfied in certain non-equilibrium granular systems under cyclic shear, challenging previous assumptions.

Contribution

The study demonstrates experimentally that detailed balance can hold in cyclically sheared granular systems, expanding its applicability beyond equilibrium conditions.

Findings

Detailed balance is satisfied in quasi-statically cyclically sheared granular systems.

The approach to detailed balance depends on system size and time.

This challenges the belief that detailed balance only applies to equilibrium systems.

Abstract

The principle of detailed balance (DB) states that every kinetic transition in a system with many micro-states, $\mu$, is balanced, on average, with the opposite transition, $\mu_i\leftrightharpoons\mu_j$. Since its introduction by Boltzmann, this principle has been used by luminaries, such as Einstein, Eddington, Kramers, Pauli, Ehrenfest, Dirac, Onsager, and many others to derive significant results that underpin much of our scientific understanding. The current belief is that DB is satisfied only in equilibrium systems, while non-equilibrium steady states can only be balanced by cycles, such as $A\to B\to C\to A$. We show here experimentally that DB can exist and is commonly and robustly satisfied in a family of quasi-statically cyclically sheared granular systems. We further study the approach to DB as a function of system size and time. Given the significant impact that this principle has had on equilibrium systems, we believe that this discovery paves the way for better models of the dynamics of non-equilibrium systems.