When an isolated system is brought in contact with a heat bath its final energy is random and follows the Gibbs distribution -- a cornerstone of statistical physics. The system's energy can also be changed by performing non-adiabatic work using a cyclic process. Almost nothing is known about the resulting energy distribution in this setup, which is especially relevant to recent experimental progress in cold atoms, ions traps, superconducting qubits and other systems. Here we show that when the non-adiabatic process comprises of many repeated cyclic processes the resulting energy distribution is universal and different from the Gibbs ensemble. We predict the existence of two qualitatively different regimes with a continuous second order like transition between them. We illustrate our approach performing explicit calculations for both interacting and non-interacting systems.
The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive part of the entropy change does not become negative. However, for any finite system and small driving, the mean entropy change can well be negative. We derive these results using as micro-canonical entropy a variant recently introduced by Swendsen and co-workers called "canonical". This canonical entropy is the one of a canonical ensemble with the correspond…
For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a fixed-temperature free energy difference, $W \ge ΔF_T$ , and a strong bound, given by a fixed-entropy internal energy difference, $W \ge ΔE_S$ . It is known that statistical inequalities related to the weak bound can be obtained from the nonequilibrium work relation, $\langle\exp (-βW)\rangle = \exp(-βΔF_T)$ . Here we derive an integral fluctuation relation $\langle\…
Spinodal decomposition in a near-critical binary fluid is examined for experimental scenarios in which the liquid is quenched abruptly by changing the pressure and the subsequent phase separation occurs with no heat flow from the outside, i.e., adiabatically. Equations of motion for the system volume and effective temperature are derived. It is shown that for this case that the nonequilibrium decomposition process is well approximated as one of constant entropy, i.e., as thermodynamically reversible. Quantitative comparison, with no adjustable parameters, is made with experimental light scatte…
Fluctuation theorems for thermally isolated driven quantum systems: nonadiabaticity, excess work and strong inequalities
Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas（坎皮纳斯州立大学格莱布·瓦塔金物理研究所）；NEST, Istituto Nanoscienze-CNR, Scuola Normale Superiore（意大利国家研究委员会纳米科学研究所）
We provide experimental evidence of universal dynamics far from equilibrium during the relaxation of an isolated one-dimensional Bose gas. Following a rapid cooling quench, the system exhibits universal scaling in time and space, associated with the approach of a non-thermal fixed point. The time evolution within the scaling period is described by a single universal function and scaling exponent, independent of the specifics of the initial state. Our results provide a quantum simulation in a regime, where to date no theoretical predictions are available. This constitutes a crucial step in the …
We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast (radiation) and slow (kink or domain wall) degrees of freedom. We find a universal long-time dynamics, largely independent of the microscopic details of the system, in which the kinks control the relaxation of relevant observables and correlations. The resulting late-time dynamics can be described by a set of phenomenological equations, which yield results …
Two approaches are outlined to characterize the fluctuation behavior of work applied to a system by a slow change of a parameter. One approach uses the adiabatic theorems of quantum and classical mechanics, the other one is based on the behavior of the correlations of the generalized coordinate that is conjugate to the changed parameter. Criteria are obtained under which the work done on small thermally isolated as well as on open systems ceases to fluctuate in a quasistatic process.
We investigate a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. We formulate a path integral in terms of thermal pure states and derive an effective action for trajectories in a thermodynamic state space, where the entropy appears with its conjugate variable. In particular, for quasi-static operations, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant.
