We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval t. A heat, which differs from a work by an energy change, is shown to satisfy a modified fluctuation relation. Modification is brought by correlation between a heat and an energy change during nonequilibrium processes whose effect may not be negligible even in the t → ∞ limit. The fluctuation relation is derived for overdamped Langevin equation systems, and tested in a linear diffusion system. Fluctuations of thermodynamic quantities of nonequilibrium systems obey a universal relation referred to as fluctuation theorem (FT) [1][2][3][4][5][6][7][8][9]. Discovery of the FT leads to a great advance in nonequilibrium statistical mechanics. Based on the FT, one can generalize the fluctuation dissipation relation to nonequilibrium systems [10][11][12] and figure out fluctuations observed in experimental small-sized systems [13][14][15].The FT for a quantity R over a time interval t takes the form e −R = 1, where the average · is taken over a probability distribution for an initial state and over all time trajectories. Some quantities further satisfy the FT in the form P r (R)/P r (−R) = e R where P r (R) = δ(R − R) is a probability density function (PDF) for a nonequilibrium process andP r (R) for a corresponding reverse process. The latter is called the detailed FT and implies the former called the integral FT.Consider a system being in thermal equilibrium with a heat reservoir. We will set the temperature and the Boltzmann constant to unity. The system is driven into a nonequilibrium state if one adds a nonconservative force or applies a time-dependent perturbation. Then, there exist nonzero net flows of a nonequilibrium work W into the system and a heat dissipation Q into the reservoir. It is well established that the work W over a time interval t obeys the FT [2,6]. In addition, the total entropy change ∆S tot = ∆S sys + ∆S res with the system (reservoir) entropy S sys (S res ) satisfies the integral FT for an arbitrary initial state, and even the detailed FT for a steady state initial condition [7]. Thermodynamic quantities are measurable experimentally from time trajectories in classical systems [16], while their experimental measurability in quantum systems is still an open issue [17].Fluctuations of heat Q, or entropy production ∆S res = Q/T , has also been attracting much interest [18][19][20][21][22][23][24][25][26]. Note that a heat differs from a work by an energy change ∆E as Q = W − ∆E. When t becomes large, the system will reach a steady state with constant work and heat production rates on average. Hence one may expect the FT for heat in the large t limit where an energy change can be negligible (Q ≃ W ≫ ∆E). In fact, the FT for the heat production rate (Q/t) is derived formally in the t → ∞ limit [3,4]. On the other hand, some model studies demonstrate the FT for heat [25] or failure of the FT in the t → ∞ limit [19,23,24]. So, it is ...

We investigate the stochastic thermodynamics of a two-particle Langevin system. Each particle is in contact with a heat bath at different temperatures T_{1} and T_{2} (

We investigate the phase transitions in a coupled system of Ising spins and a fluctuating network. Each spin interacts with q neighbors through links of the rewiring network. The Ising spins and the network are in thermal contact with the heat baths at temperatures T_{S} and T_{L}, respectively, so the whole system is driven out of equilibrium for T_{S}≠T_{L}. The model is a generalization of the q-neighbor Ising model [A. Jędrzejewski et al., Phys. Rev. E 92, 052105 (2015)PLEEE81539-375510.1103/PhysRevE.92.052105], which corresponds to the limiting case of T_{L}=∞. Despite the mean-field nature of the interaction, the q-neighbor Ising model was shown to display a discontinuous phase transition for q≥4. Setting up the rate equations for the magnetization and the energy density, we obtain the phase diagram in the T_{S}-T_{L} parameter space. The phase diagram consists of a ferromagnetic phase and a paramagnetic phase. The two phases are separated by a continuous phase transition belonging to the mean-field universality class or by a discontinuous phase transition with an intervening coexistence phase. The equilibrium system with T_{S}=T_{L} falls into the former case while the q-neighbor Ising model falls into the latter case. At the tricritical point, the system exhibits the mean-field tricritical behavior. Our model demonstrates a possibility that a continuous phase transition turns into a discontinuous transition by a nonequilibrium driving. Heat flow induced by the temperature difference between two heat baths is also studied.

A Brownian information engine is a device extracting mechanical work from a single heat bath by exploiting the information on the state of a Brownian particle immersed in the bath. As for engines, it is important to find the optimal operating condition that yields the maximum extracted work or power. The optimal condition for a Brownian information engine with a finite cycle time τ has been rarely studied because of the difficulty in finding the nonequilibrium steady state. In this study, we introduce a model for the Brownian information engine and develop an analytic formalism for its steady-state distribution for any τ. We find that the extracted work per engine cycle is maximum when τ approaches infinity, while the power is maximum when τ approaches zero.

In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called 'friction'. To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We exactly solve them and compare the performance of the Agarwal engine with that of the Lidbladian one. Particularly, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasi-static limit with the Otto efficiency, and the power of the Lindbladian engine can be non-zero in the short-time limit. Based on additional numerical calculations of these outcomes, we discuss possible origins of such differences between two engines and reveal them. Our results imply that even with equilibrium bath, a non-equilibrium working fluid brings on the higher performance than what an equilibrium one does.