. Author manuscript; available in PMC: 2006 Aug 14.

Published in final edited form as: Chem Phys Lett. 2005 Jul 20;410(4-6):430–435. doi: 10.1016/j.cplett.2005.06.002

Table 1.

HSMC results for the entropy of N-bond SAWs obtained from n reconstructions of a straight chain. S^A [Eq. (10)] and S^B [Eq. (11)] are upper and lower bounds, respectively, S^M [Eq. (12)] is their average, and S^D [Eq. (13)] is an exact entropy functional. σ_A [Eq. (6)] is the fluctuation and n_future is related to the number of MC steps per bond (see text). S_TI and S_scan and S_series were obtained by thermodynamic integration, the scanning method [15], and a series expansion formula (see text), respectively. The statistical error is defined by parentheses: 1.00(3) = 1.00 ± 0.03.

n_future	S^A / k_B	σ_A	S^B / k_B	S^M / k_B	S^D / k_B	n
N = 49 S_SCAN = 1.000904 (4)
500	1.00583 (1)	0.01424 (2)	0.99602 (5)	1.00093 (3)	1.00091 (3)	1250000
5000	1.00140 (1)	0.00448 (2)	1.00042 (3)	1.00091 (2)	1.00091 (2)	125000
50000	1.00095 (1)	0.00142 (2)	1.00085 (3)	1.00090 (2)	1.00090 (2)	12500
S_TI	1.000897 (3)		1.000897 (3)	1.000897 (3)	1.000897 (3)
Sseries	1.000899 (4)		1.000899 (4)	1.000899 (4)	1.000899 (4)
N = 99 S_SCAN = 0.987726 (5)
500	0.99294 (2)	0.01030 (3)	0.9826 (1)	0.98775 (5)	0.98773 (5)	250000
5000	0.98826 (2)	0.00324 (3)	0.98722 (5)	0.98774 (3)	0.98774 (3)	25000
50000	0.98777 (2)	0.00101 (3)	0.98767 (4)	0.98772 (2)	0.98772 (3)	2500
S_TI	0.987727 (3)		0.987727 (3)	0.987727 (3)	0.987727 (3)
Sseries	0.987730 (3)		0.987730 (3)	0.987730 (3)	0.987730 (3)
N = 149 S_SCAN = 0.982740 (3)
500	0.98806 (2)	0.00852 (3)	0.9774 (2)	0.9827 (1)	0.9827 (1)	250000
5000	0.98329 (2)	0.00267 (3)	0.98222 (5)	0.98276 (3)	0.98276 (3)	25000
50000	0.98281 (2)	0.00085 (3)	0.98270 (4)	0.98275 (2)	0.98275 (3)	2500
S_TI	0.982742 (3)		0.982742 (3)	0.982742 (3)	0.982742 (3)
Sseries	0.982740 (2)		0.982740 (2)	0.982740 (2)	0.982740 (2)
N = 249 S_SCAN = 0.97836 (2)
500	0.98391 (3)	0.00669 (4)	0.9727 (3)	0.9783 (2)	0.9783 (2)	63000
5000	0.97889 (2)	0.00208 (4)	0.97782 (8)	0.97836 (4)	0.97836 (5)	9100
50000	0.97840 (2)	0.00066 (4)	0.97829 (5)	0.97835 (3)	0.97835 (3)	930
S_TI	0.978358 (4)		0.978358 (4)	0.978358 (4)	0.978358 (4)
Sseries	0.978360 (1)		0.978360 (1)	0.978360 (1)	0.978360 (1)
N = 399 S_SCAN = 0.97567 (4)
500	0.98138 (6)	0.00540 (5)	0.9710 (5)	0.9762 (3)	0.9759 (3)	9500
5000	0.97625 (4)	0.00170 (5)	0.9751 (1)	0.97567 (5)	0.97567 (5)	2000
50000	0.97568 (4)	00.00053 (5)	0.97557 (7)	0.97563 (4)	0.97563 (5)	225
S_TI	0.975655 (8)		0.975655 (8)	0.975655 (8)	0.975655 (8)
Sseries	0.975652(1)		0.975652 (1)	0.975652 (1)	0.975652 (1)
N = 599 S_SCAN = 0.97395 (5)
500	0.98003 (8)	0.00445 (7)	0.9706 (8)	0.9753 (4)	0.9748 (5)	3000
5000	0.97466 (7)	0.00139 (7)	0.9736 (2)	0.9741 (1)	0.9741 (1)	450
50000	0.97413 (5)	0.00036 (7)	0.9741 (1)	0.97409 (6)	0.97409 (5)	45
S_TI	0.97404 (1)		0.97404 (1)	0.97404 (1)	0.97404 (1)
Sseries	0.974025(1)		0.974025(1)	0.974025(1)	0.974025(1)