A hot cup of coffee or a glass of cold drinks left sitting in a room is in a transient out-of-equilibrium state that relaxes towards thermal equilibrium by exchanging heat with the surrounding gas molecules. When coupled to multiple environments, such systems can stay out of equilibrium for an arbitrarily long time. For example, a thermal conductor connected to two heat reservoirs at different temperatures reaches a nonequilibrium stationary state where heat flows at a constant rate from the hot reservoir to the cold reservoir through the conductor.

A system can also be inherently nonequilibrium because of its dynamics. For example, an athermal system like a continually shaken box of marbles reaches a nonequilibrium stationary state where the velocity distribution is not typically Maxwell-Boltzmann. Another example of broad interest is the so-called *active motion*, found in living systems ranging from bacterial motility at the microscopic scale to the flocking of birds and fish schools at the macroscopic scale as well as in artificial systems including self-catalytic swimmers, and nanomotors.

In fact, only a tiny subset of stochastic dynamics—of a very particular kind that satisfies detailed balance—leads to equilibrium. For this reason, nonequilibrium processes are ubiquitous, and the scope of nonequilibrium statistical physics extends far beyond thermal systems. In addition to the physical sciences, stochastic processes have applications across diverse other disciplines, ranging from biological and environmental sciences, financial markets to vehicular traffic.

Unlike the Boltzmann-Gibbs distribution for a system at thermal equilibrium, the probabilities of the microscopic configurations of a nonequilibrium system are not given *a priori*. These are to be determined from the underlying stochastic dynamics, which is often challenging due to the lack of a general framework.

I am interested in various aspects of nonequilibrium systems and stochastic processes, focusing on fundamental understanding as well as practical applications.

See my research page for highlights and publications for details.

The motion of a **Brownian particle** [], a **run and tumble particle** [], an **active Brownian particle** [], and a **direction reversing active Brownian particle** [] in two dimensions.

I like to study such stochastic processes arising in various physical contexts.

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